mime_content_type

Fast generation of uptodate mime types:
<?php
define('APACHE_MIME_TYPES_URL','http://svn.apache.org/repos/asf/httpd/httpd/trunk/docs/conf/mime.types');
function generateUpToDateMimeArray($url){
 $s=array();
 foreach(@explode("\n",@file_get_contents($url))as $x)
 if(isset($x[0])&&$x[0]!=='#'&&preg_match_all('#([^\s]+)#',$x,$out)&&isset($out[1])&&($c=count($out[1]))>1)
 for($i=1;$i<$c;$i++)
 $s[]='&nbsp;&nbsp;&nbsp;\''.$out[1][$i].'\' => \''.$out[1][0].'\'';
 return @sort($s)?'$mime_types = array(<br />'.implode($s,',<br />').'<br />);':false;
}
echo
generateUpToDateMimeArray(APACHE_MIME_TYPES_URL);
?>

Output:
$mime_types = array(
 '123' => 'application/vnd.lotus-1-2-3',
 '3dml' => 'text/vnd.in3d.3dml',
 '3g2' => 'video/3gpp2',
 '3gp' => 'video/3gpp',
 '7z' => 'application/x-7z-compressed',
 'aab' => 'application/x-authorware-bin',
 'aac' => 'audio/x-aac',
 'aam' => 'application/x-authorware-map',
 'aas' => 'application/x-authorware-seg',
...
Enjoy.

I also had issues with this function.
The issue was that it would almost always return "text/plain".
echo ini_get('mime_magic.magicfile'); // returns /etc/httpd/conf/magic
I found that I needed the OS' magic.mime file instead.
You can either copy it to the existing location, or update your php.ini, you cannot use ini_set().
[root@blade conf]# mv magic magic.old
[root@blade conf]# cp /usr/share/magic.mime magic
[root@blade conf]# apachectl graceful
Note: you will see that I have gracefully restarted apache to ensure it has taken affect.

There is a composer package that will do this:
https://github.com/ralouphie/mimey
<?php
$mimes = new \Mimey\MimeTypes;
// Convert extension to MIME type:
$mimes->getMimeType('json'); // application/json
// Convert MIME type to extension:
$mimes->getExtension('application/json'); // json

Lukas V is IMO missing some point. The MIME type of a file may not be corresponding to the file suffix.
Imagine someone would obfuscate some PHP code in a .gif file, the file suffix would be 'GIF' but the MIME would be text/plain or even text/html.
Another example is files fetched via a distant server (wget / fopen / file / fsockopen...). The server can issue an error, i.e. 404 Not Found, wich again is text/html, whatever you save the file to (download_archive.rar).
His provided function should begin by the test of the function existancy like :
function MIMEalternative($file)
{
 if(function_exists('mime_content_type'))
 return mime_content_type($file);
 else
 return <lukas_v.MIMEfunction>($file);
}

using 
<?php
function detectFileMimeType($filename='')
{
 $filename = escapeshellcmd($filename);
 $command = "file -b --mime-type -m /usr/share/misc/magic {$filename}";
 $mimeType = shell_exec($command);
 
 return trim($mimeType);
}
?>
should work on most shared linux hosts without errors. It should also work on Windows hosts with msysgit installed.

I see a lot of comments suggesting doing file extension sniffing (i.e. assuming .jpg files are JPEG images) when proper file-type sniffing functions are unavailable.
I want to point out that there is a much more accurate way.
If neither mime_content_type() nor Fileinfo is available to you and you are running *any* UNIX variant since the 70s, including Mac OS, OS X, Linux, etc. (and most web hosting is), just make a system call to 'file(1)'.
Doing something like this:
<?php
echo system("file -bi '<file path>'");
?>
will output something like "text/html; charset=us-ascii". Some systems won't add the charset bit, but strip it off just in case.
The '-bi' bit is important. However, you can use a command like this:
<?php
echo system("file -b '<file path>'"); // without the 'i' after '-b'
?>
to output a human-readable string, like "HTML document text", which can sometimes be useful.
The only drawback is that your scripts will not work on Windows, but is this such a problem? Just about all web hosts use a UNIX.
It is a far better way than just examining the file extension.

<?php
if(!function_exists('mime_content_type')) {
 function mime_content_type($filename) {
 $mime_types = array(
 'txt' => 'text/plain',
 'htm' => 'text/html',
 'html' => 'text/html',
 'php' => 'text/html',
 'css' => 'text/css',
 'js' => 'application/javascript',
 'json' => 'application/json',
 'xml' => 'application/xml',
 'swf' => 'application/x-shockwave-flash',
 'flv' => 'video/x-flv',
 // images
 'png' => 'image/png',
 'jpe' => 'image/jpeg',
 'jpeg' => 'image/jpeg',
 'jpg' => 'image/jpeg',
 'gif' => 'image/gif',
 'bmp' => 'image/bmp',
 'ico' => 'image/vnd.microsoft.icon',
 'tiff' => 'image/tiff',
 'tif' => 'image/tiff',
 'svg' => 'image/svg+xml',
 'svgz' => 'image/svg+xml',
 // archives
 'zip' => 'application/zip',
 'rar' => 'application/x-rar-compressed',
 'exe' => 'application/x-msdownload',
 'msi' => 'application/x-msdownload',
 'cab' => 'application/vnd.ms-cab-compressed',
 // audio/video
 'mp3' => 'audio/mpeg',
 'qt' => 'video/quicktime',
 'mov' => 'video/quicktime',
 // adobe
 'pdf' => 'application/pdf',
 'psd' => 'image/vnd.adobe.photoshop',
 'ai' => 'application/postscript',
 'eps' => 'application/postscript',
 'ps' => 'application/postscript',
 // ms office
 'doc' => 'application/msword',
 'rtf' => 'application/rtf',
 'xls' => 'application/vnd.ms-excel',
 'ppt' => 'application/vnd.ms-powerpoint',
 // open office
 'odt' => 'application/vnd.oasis.opendocument.text',
 'ods' => 'application/vnd.oasis.opendocument.spreadsheet',
 );
 $ext = strtolower(array_pop(explode('.',$filename)));
 if (array_key_exists($ext, $mime_types)) {
 return $mime_types[$ext];
 }
 elseif (function_exists('finfo_open')) {
 $finfo = finfo_open(FILEINFO_MIME);
 $mimetype = finfo_file($finfo, $filename);
 finfo_close($finfo);
 return $mimetype;
 }
 else {
 return 'application/octet-stream';
 }
 }
}
?>

Completing <some dude AT somewhere DOT com> comment:
0 string < ? php application/x-httpd-php
and string detection on text files may fail if you check a file encoded with signed UTF-8. The UTF-8 signature is a two bytes code (0xFF 0xFE) that prepends the file in order to force UTF-8 recognition (you may check it on an hexadecimal editor).

For me mime_content_type didn't work in Linux before I added 
mime_magic.magicfile = "/usr/share/magic.mime"
to php.ini (remember to find the correct path to mime.magic)

Converting mime types to extension in php (by Alex Corvi) :
https://gist.github.com/alexcorvi/df8faecb59e86bee93411f6a7967df2c 

Regarding serkanyersen's example : It is advisable to change the regular expression to something more precise like
preg_match("|\.([a-z0-9]{2,4})$|i", $filename, $m);
This makes sure that only the last few characters are taken. The original expression would not work if the filename is a relative path.

if you use a transparent 'spacer' GIF i've found it needs to be a around 25x25 for it to register as 'image/gif'. otherwise it's read in as 'text/plain'.

I added these two lines to my magic.mime file:
0 string \<?php application/x-httpd-php
0 string \<?xml text/xml
The first one may not work if "<?php" is not at the very beginning of your file, e.g., if some HTML preceeds the first bit of PHP code. The second one should work because "<?xml" *should* be the first thing in every XML file.

Here's a simple function to return MIME types, based on the Apache mime.types file. [The one in my previous submission, which has since been replaced by this one] only works properly if mime.types is formatted as Windows text. The updated version below corrects this problem. Thanks to Mike for pointing this out.
<?php
function get_mime_type($filename, $mimePath = '../etc') {
 $fileext = substr(strrchr($filename, '.'), 1);
 if (empty($fileext)) return (false);
 $regex = "/^([\w\+\-\.\/]+)\s+(\w+\s)*($fileext\s)/i";
 $lines = file("$mimePath/mime.types");
 foreach($lines as $line) {
 if (substr($line, 0, 1) == '#') continue; // skip comments
 $line = rtrim($line) . " ";
 if (!preg_match($regex, $line, $matches)) continue; // no match to the extension
 return ($matches[1]);
 }
 return (false); // no match at all
}
?>

Notes:
[1] Requires mime.types file distributed with Apache (normally found at ServerRoot/conf/mime.types). If you are using shared hosting, download the file with the Apache distro and then upload it to a directory on your web server that php has access to.
[2] First param is the filename (required). Second parameter is path to mime.types file (optional; defaults to home/etc/).
[3] Based on MIME types registered with IANA (http://www.iana.org/assignments/media-types/index.html). Recognizes 630 extensions associated with 498 MIME types.
[4] Asserts MIME type based on filename extension. Does not examine the actual file; the file does not even have to exist.
[5] Examples of use:
>> echo get_mime_type('myFile.xml');
>> application/xml
>> echo get_mime_type('myPath/myFile.js');
>> application/javascript
>> echo get_mime_type('myPresentation.ppt');
>> application/vnd.ms-powerpoint
>> echo get_mime_type('http://mySite.com/myPage.php);
>> application/x-httpd-php
>> echo get_mime_type('myPicture.jpg');
>> image/jpeg
>> echo get_mime_type('myMusic.mp3');
>> audio/mpeg
and so on...
To create an associative array containing MIME types, use:
<?php
function get_mime_array($mimePath = '../etc')
{
 $regex = "/([\w\+\-\.\/]+)\t+([\w\s]+)/i";
 $lines = file("$mimePath/mime.types", FILE_IGNORE_NEW_LINES);
 foreach($lines as $line) {
 if (substr($line, 0, 1) == '#') continue; // skip comments
 if (!preg_match($regex, $line, $matches)) continue; // skip mime types w/o any extensions
 $mime = $matches[1];
 $extensions = explode(" ", $matches[2]);
 foreach($extensions as $ext) $mimeArray[trim($ext)] = $mime;
 }
 return ($mimeArray);
}
?>

The correct little correction:
exec will return the mime with a newline at the end, the trim() should be called with the result of exec, not the other way around.
<?php
if ( ! function_exists ( 'mime_content_type ' ) )
{
 function mime_content_type ( $f )
 {
 return trim ( exec ('file -bi ' . escapeshellarg ( $f ) ) ) ;
 }
}
?>

// Here is a working version of a function that fetches the meme types from apache's built in mime list and creates an array of which the keys are the file extensions:
function generateUpToDateMimeArray($url){
 $return = array();
 $mimes = file_get_contents('http://svn.apache.org/repos/asf/httpd/httpd/trunk/docs/conf/mime.types'); // make sure that allow_url_fopen is enabled!
 preg_match_all('#^([^\s]{2,}?)\s+(.+?)$#ism', $mimes, $matches, PREG_SET_ORDER);
 
 foreach ($matches as $match){
 $exts = split(" ", $match[2]);
 foreach ($exts as $ext){
 $return[$ext]=$match[1];
 }
 }
 return $return;
}
// usage:
$typeMime = generateUpToDateMimeArray();
echo $typeMime['gif'];

The function mime_content_type only worked for me on Microsoft Windows after I added the directive "mime_magic.debug" to my php.ini with the value of "On". The default value appears to be "Off". Exampe:
[mime_magic]
mime_magic.debug = On
mime_magic.magicfile = "c:\php\extras\magic.mime"

Slight improvement over Josh Sean's code: this makes a usable and formatted php file containing the latest mime associations ( strictly using the file extension) in an array or if the file_get_contents fails ( say you are offline ) leaves the original file alone. 
I made it a bit "dummer" for readability purposes, don't judge me just improve it on your own.
<?php
define('APACHE_MIME_TYPES_URL','http://svn.apache.org/repos/asf/httpd/httpd/trunk/docs/conf/mime.types');
function generateUpToDateMimeArray($url){
 $s=array();
 $result = @file_get_contents($url);
 if ($result == FALSE )
 {
 $returned = "ERROR";
 }
 else
 {
 foreach(@explode("\n",$result)as $x)
 {
 if(isset($x[0])&&$x[0]!=='#'&&preg_match_all('#([^\s]+)#',$x,$out)&&isset($out[1])&&($c=count($out[1]))>1)
 for($i=1;$i<$c;$i++)
 $s[]=' \''.$out[1][$i].'\' => \''.$out[1][0].'\'';
 }
 $returned = @sort($s)?'<?php' . "\n" . '$mime_types = array(' . "\n" . implode($s,",\n") . "\n);\n" . '?>':false;
 }
 return $returned;
}
 $file_name = 'mime-array.php';
 $data = generateUpToDateMimeArray(APACHE_MIME_TYPES_URL);
 
 if ($data != "ERROR")
 {
 $file = fopen($file_name, 'wb') or die("cannot open $file_name\n");
 fwrite($file, $data ) or die("cannot write data\n");
 fclose($file);
 echo "updated";
 }
 else
 {
 echo "faliure";
 }
?>
All you need to do is run it once and in your code you can simply add these two lines:
<?php
include 'mime-array.php';
global $mime_types;
?>

enjoy

<?PHP
 function qmimetype($file) {
 $ext=array_pop(explode('.',$file));
 foreach(file('/usr/local/etc/apache22/mime.types') as $line)
 if(preg_match('/^([^#]\S+)\s+.*'.$ext.'.*$/',$line,$m))
 return $m[1];
 return 'application/octet-stream';
 }
?>

Not perfect, but works good enough for me ;)