Since this is more of a general 'all things WWI' area (judging by the books thread), I thought I'd chip in with what little I know of for WWI games:
Starting with naval matters, there's Avalanche Press' Great War at Sea series. I only have Plan Orange, which is about a hypothetical war between US and Japan in the '30s. But the original two games are the Mediterranean and North Sea during WWI.
It's basically a simple operational level game with tactical combat resolution. The tactical level isn't bad; they try to keep it simple since it's not the only focus of the game, so they ignore facing, firing arcs and the like in 15 minute turns (generally enough for maneuvers to be done in). But the 'simple' aspect is wrecked by a poorly-presented impulse system, and all the ships have paperwork in the form of check-off box hit records. I haven't done anything with the operational-level stuff, but orders are generally given in advance, and there's some hidden movement. Fuel stores and the like are tracked.
It's generally well regarded, and it is good, spawning several games, and the spinoff Second World War at Sea series. I'd try to go for one of the later releases first, as it takes Avalanche a while to pound their rules into good shape.
Grand strategy has had a number of entries over the decades, but the big winner there is Paths of Glory from GMT. A classic Card-Driven design, it's not bad history, and a very good game (and there's a few variants aimed at promoting more historical play). Naval affairs are just a couple of card plays—Blockade, U-boats and a couple others.
The spinoff Pursuit of Glory takes the same system and applies it just to the Middle East+Turkey, and is one of my all-time favorite games. Both players sit down to the board, look at it, and say, 'I'm screwed'. It has a lot more chrome than Paths, but I think it all makes it a better game, and I find Paths a bit bland. The British can bring in forces for invasions, and get to choose when and where to come ashore.
Operational-level games have been popular recently, and there's been a number of WWI titles. All of them are focused on the land war of course. The simplest would be the Clash of Giants series from GMT. I've only played one out of the four scenarios available (Galicia), but really enjoyed it with rolling to see just how active different formations are each turn.
MMP released A Victory Complete (Tannenburg) as part of an issue of Operations magazine, which uses the same general chit-pull system as A Victory Lost. I understand AVC is pretty good, but of the various games in the system, I've only ever played AVL, which is great.
GMT also has a series that goes into great detail at the operational level, taking a look at how units get worn out, and need to draw their supplies from their corps headquarters, and all deal with just the initial campaigns. I've looked at the original 1914: Twilight in the East, which is a real monster game, and it looks very impressive. Serbien muß sterbien is a much more manageable size. A couple of my friends like the series, though I haven't managed to have them teach it to me yet.
Der Weltkrieg came out a couple years ago, and I just picked up the Ottoman front game for cheap, but haven't had a good chance to look it over yet. Main thing is all terrain effects are by hexside rather than hex interior. I'd have to actually play it to see how well that works out.
I know there's a few more tactically-oriented games, but I haven't payed much attention. GMT's upcoming Gallipoli, 1915 is grand tactical, and is looking interesting from the playtest reports I've seen.
