What are all the possible values for HTTP "Content-Type" header?

You can find every content type here: http://www.iana.org/assignments/media-types/media-types.xhtml

The most common type are:

1. Type application

   application/java-archive
   application/EDI-X12   
   application/EDIFACT   
   application/javascript   
   application/octet-stream   
   application/ogg   
   application/pdf  
   application/xhtml+xml   
   application/x-shockwave-flash    
   application/json  
   application/ld+json  
   application/xml   
   application/zip  
   application/x-www-form-urlencoded  
   

2. Type audio

   audio/mpeg   
   audio/x-ms-wma   
   audio/vnd.rn-realaudio   
   audio/x-wav   
   

3. Type image

   image/gif   
   image/jpeg   
   image/png   
   image/tiff    
   image/vnd.microsoft.icon    
   image/x-icon   
   image/vnd.djvu   
   image/svg+xml    
   

4. Type multipart

   multipart/mixed    
   multipart/alternative   
   multipart/related (using by MHTML (HTML mail).)  
   multipart/form-data  
   

5. Type text

   text/css    
   text/csv    
   text/html    
   text/javascript (obsolete)    
   text/plain    
   text/xml    
   

6. Type video

   video/mpeg    
   video/mp4    
   video/quicktime    
   video/x-ms-wmv    
   video/x-msvideo    
   video/x-flv   
   video/webm   
   

7. Type vnd :

   application/vnd.android.package-archive
   application/vnd.oasis.opendocument.text    
   application/vnd.oasis.opendocument.spreadsheet  
   application/vnd.oasis.opendocument.presentation   
   application/vnd.oasis.opendocument.graphics   
   application/vnd.ms-excel    
   application/vnd.openxmlformats-officedocument.spreadsheetml.sheet   
   application/vnd.ms-powerpoint    
   application/vnd.openxmlformats-officedocument.presentationml.presentation    
   application/msword   
   application/vnd.openxmlformats-officedocument.wordprocessingml.document   
   application/vnd.mozilla.xul+xml   
   

As is defined in RFC 1341:

In the Extended BNF notation of RFC 822, a Content-Type header field value is defined as follows:

Content-Type := type "/" subtype *[";" parameter]

type := "application" / "audio" / "image" / "message" / "multipart" / "text" / "video" / x-token

x-token := < The two characters "X-" followed, with no intervening white space, by any token >

subtype := token

parameter := attribute "=" value

attribute := token

value := token / quoted-string

token := 1*<any CHAR except SPACE, CTLs, or tspecials>

tspecials := "(" / ")" / "<" / ">" / "@" ; Must be in / "," / ";" / ":" / "" / <"> ; quoted-string, / "/" / "[" / "]" / "?" / "." ; to use within / "=" ; parameter values

And a list of known MIME types that can follow it (or, as Joe remarks, the IANA source).

As you can see the list is way too big for you to validate against all of them. What you can do is validate against the general format and the type attribute to make sure that is correct (the set of options is small) and just assume that what follows it is correct (and of course catch any exceptions you might encounter when you put it to actual use).

Also note the comment above:

If another primary type is to be used for any reason, it must be given a name starting with "X-" to indicate its non-standard status and to avoid any potential conflict with a future official name.

You'll notice that a lot of HTTP requests/responses include an X- header of some sort which are self defined, keep this in mind when validating the types.

I would aim at covering a subset of possible "Content-type" values, you question seems to focus on identifying known content types.

@Jeroen RFC 1341 reference is great, but for an fairly exhaustive list IANA keeps a web page of officially registered media types here.