I'm still new to the game and have only played against the AIs so far. In my experience the AI races aren't bad for AIs, but generally are still no match for a semi-experienced human player. Certain game settings, however, can improve the AIs' chances:
(1) As Douglas has suggested, play against the top races from the AI Deathmatch run by Master Belisarius. Five of the top six finishers are found in the TDM ModPack; these are the ones I'm playing against now.
(2) It seems unmodded AIs will accept trades even when at war. Don't use this exploit.
(3) Play a semi-generic race, i.e. don't
Min-Max your race aggressively.
(4) Select "Team Play" during game setup. The AIs will all declare war on the human within a turn or two of first contact.
(5) Play with simultaneous movement and strategic combat. Sequential turns and tactical combat give the human player a big advantage.
(6) Give the AIs a bonus. As I recall, the AI Deathmatch was run with low bonus for all AIs. Players should start with "Good" homeworlds.
(7) Play in a smaller quadrant. The AIs tend to expand slower than human players, but in a small/medium quadrant conflicts start before the AIs fall far behind.
Some combination of these settings should challenge or even overwhelm a new player; they can be adjusted as player skill improves.