Jason Schaff

That question is a little vague. You might want to consider if you have preferences for era (ancient, napoleonic, civil war, WW II, modern, etc), scale (tactical, operational, strategic, grand strategic), and size (how big a game, with how many pieces, etc. are you willing to deal with). In any case, here goes my list of faves:

Third World War Series (4 games - 3rd World War, Arctic Front, Southern Front, Persian Gulf, published by GDW (R.I.P.) out of print) Strategic level sim of a 1980's NATO-Warsaw Pact conflict in Europe and the Mid-East. Moderate complexity. The games can be played independently, or combined for a monster campaign.

Great Battles of History Series (published by GMT, something like 8 titles, some in print, some not, my personal favorites are SPQR and Great Battles of Alexander, both OOP). Tactical level sims of warfare from the ancient world to the very early gunpowder period. Fairly complex, but the rules are well written. Each game includes multiple scenarios, and most scenarios play on a single map.

Panzer Grenadier Series (3 titles - Panzer Grenadier, Heroes of the Soviet Union, and Airborne, published by Avalanche Press, in print) Tactical level sim of WW II ground combat, with multiple scenarios in each game. Fairly low complexity, and most scenarios are quite small.

TacOps (computer game published by Battlefront.com, in print) Tactical sim of modern ground warfare designed by a retired US Marine major. Multiple scenarios with a wide range of size and complexity. The game is functionally easy to play, but many of the scenarios are _very_ hard to win. I very highly recommend this one if the subject matter interests you.

Axis & Allies (published by Milton Bradley, in print) A very simple grand strategic "sim" of WW II. A great "beer & pretzels" game. Fun to play, with lots of plastic minis, but not much depth. There are also "daughter" games, A&A Europe and A&A Pacific, covering the individual theaters. I like Europe, but haven't tried Pacific yet.

Chris von Seggern

At one time I was I'm the miscreant responsible for suggesting ASL-—forget I ever said that. It's a great game, but you definitely need to have some wargaming experience under your belt before you could possibly enjoy ASL. It's just too big a headache to assimilate if you aren't already in the hobby.

Some people have suggested Battle Cry. That's an excellent idea. Battle Cry is really about half-wargame, half-boardgame, but it at least introduces a hex map, terrain types, and different units having different abilities.

I can also second the suggestions about GMT games. They're very, very good in general. Any of the ones people here have suggested (We the People, Reds!, Paths of Glory, etc.) are great. One thing about the GMT games is that they incorporate more of a strategic perspective than a tactical, much of the time. If you're looking for that aspect in a game, they're probably the best way to go. We the People is IMHO the simplest of the bunch, and might be a good starting point.

You might also look at Avalanche, especially if you're interested in naval warfare. The Great War at Sea series are all very playable and very well-done, plus they have excellent graphics on the maps and counters.