allegro/directx

DirectX:
+Microsoft product and thus widely known, especially by companies that hire game programmers.

-Game companies typically care more about specific capabilities (networking, AI, etc,) and don't necessarily care how it is achieved, especially if they are going for cross platform. Many use OpenGL, or even plug in Java, let alone Allegro.

+DirectX has good support for 3D graphics, sound, networking, and input devices for the Windows platform. It is fast.

+DirectX is very much C++ based.

-Some might say DirectX is a tad overly complicated, and is especially hard to learn for someone who could otherwise be concentrating on game and graphic theory instead of having most of their code "copied out of a book and hope it works".

+Strong community, corporate based - it is here to stay.

Allegro:
+Uses the best lib for any given platform. Wraps up DirectX and/or OpenGL, thus it is exactly just as fast.

+Cross platform. The only C/C++ lib out there that I know of, where you can compile on Windows, DOS, BeOS, and Linux (with possible ports coming up for PalmOS, WindowsCE, Dreamcast, and Mac), without changing a single line of code .

+Easy to learn and thus you can get into the actual game design and making instead of wondering how or why to do some simple technical detail. Very well documented API and plenty of examples. (Turn your program into a screen saver within ten minutes.) (Also lots of cool tools to help you make/import fonts, make your own dat files, etc...)

-Not as well known (yet) as DirectX. Version 4 just came out, and it represents the first commercially viable "final" version.

+Lots of plugins, from 3D graphics with AllegGL to MP3 playing routines.. all of which are guaranteed cross platform.

+Huge, supportive community. The lib is here to stay and improve.

+Much easier to move into other libs like DirectX after being exposed to the easy and concepts brought by using Allegro.

Obviously, I am biased, however. ;)

-Justin