It could be nice for playing ~1990 games that actually can't run well on faster machines — this is why other people have mentioned Ultima 7 and Wing Commander. Both games are notoriously speed-sensitive, so this is one of the main reasons people build 386 systems at all.
Other than that you can try some other RPGs (like Lands of Lore or Eye of the Beholder) and adventure games like Monkey Island series or Space/King/Police quest. There should also be some flight simulators for a 386. Most FPS games (besides Wolfenstein 3D) won't run well on a 386, so probably no Doom and Duke Nukem 3D.
AWE64 Gold is a really nice sound card, but it's sort of useless for a 386. It has nice General MIDI music (that only gained prominence around 1995 or so) and not-so-nice AdLib implementation. Also a lot of its features require Windows. All in all, you might want to use this card in a Pentium machine.