We the People - Already been mentioned, but is worth mentioning again - it's a wonderfully playable system, quite simple, and a good topic. Very highly recommended as an intro game. The later two (now three) games - Hannibal, Successors (3-4 players), and now For the People - are all better gamer's games, but they are non-trivially complicated and IMHO a bit of a jump from A&A. If you're coming from A&A, I'd start with WtP - it's a bit simple, but a great game in its own right.

Storm over Arnhem - Another game in which later titles using the same system are better, but the original is still simple, clean, and a great game. This is a game that I'd love to see retrofit with some ideas from Turning Point: Stalingrad and Breakout: Normandy, but be that as it may, Storm over Arnhem is an excellent, interactive, exciting game that is not very complex. It's a great battle too (who can resist playing the Red Devils at Arnhem?). If it's a winner, you can move on to Thunder at Casino, Turning Point: Stalingrad, and Breakout: Normandy which are (IMHO) progressively better games although also progressively more complex (TAC is definitely SOA-ish, but a lot longer while TP:S and B:N are higher-level and similar but different). SOA is currently available fairly cheaply as a folio from AH, so get 'em while you can.

Wooden Ships & Iron Men - A classic. Simple yet scalable; you can always make in more complex by adding optional rules or playing some of the monster engagements. The basic system is simple yet has a nice historical feel and works as a game. Trireme is also recommended but out of print.

I also would think about recommending the original Squad Leader and Up Front. No, at the end of the day they aren't simple, but they do use the very helpful programmed instructions so you can be playing the first few scenarios very easily and you can ramp up. Check out www.gro-gnard.com for more details on these games. Certainly not for everyone, but worth thinking about. Those would be my picks.

One more thought, if you're moving from A&A, Hitler's War might be a good title. I remember that I was never a big fan - the whole system was a little bit wonky for me, but it is comparatively simple and it is the same subject area and better than A&A. I'd recommend the above games more highly, but if you want to stick to the same subject material you might check out HW.