I suggest u try Tamer Saga out. I’ve been playing this game on facebook for about 2 months. It is a combination of role-playing game and strategy game featuring a fantastic world with delicate graphics and cute images.
You should try this online business game, named MarketGlory. It got me interested from the first time I played it. The more you play, the more options you have, and you can convert your virtual currency into real money, too. I am so glad that there are browser-based business games, too, nowadays. With just a few minutes of your time a day, you can make pretty much extra money.
jeez... really... no one mentioned one of the best strategy games out there?
Dawn of War and company of heroes. COH is more like Starcraft but it's a little more realistc.. it has a cover system and units such as infantry are numbered up in squads. Dawn of War 2 is also another great game.. it has a cover system, a melee system.. it's downright epic.
Now for the juggernaught of all strategy games.
Shogun 2 Total war
this video is all ingame created through the replay system. what's not to love? 1000s of troops on screen fighting to the death
Endless Space (basically a more modern master of orion, I guess> maybe not quite as good, but probably the best space 4x for a beginner. on steam) Commander: The Great War (WWI turn based hex grid grand strategy game. Easy to get into, hard to master. on matrixgames.) Shogun II: Total War (probably the best AAA strategy game right now. Has some flaws, but there's nothing that can match it for polish/spectacle, anyway. on steam.) Alea Jacta Est (grand strategy game set in the Ancient Roman period (obviously). kinda hardcore, not recommended if you're just getting into grognard wargames. on greenlight atm) Panzer Corps (basically a remake/spiritual successor of the awesome Panzer General games, which are easy to get into, but hard to master, like all good strategy games. turn based hex grid. get it on matrixgames) Xcom: Enemy Unknown (really polished/modernised version of the first xcom game from way back when. easy to get into, hard to master. on steam) Distant Worlds, ginormous space 4x. really damn complex. there's a lets play of it on the lparchive that should give you an idea of if this is for you. on matrixgames) Solium Infernum (turn-based strategy. basically a computerised board game. The Rockpapershotgun writers wrote a great series of articles chronicling one of their playthroughs of this game. check it out. Matrixgames... I think) Scourge of War: Gettysburg, (like Total War meets Sid Meier's Gettysburg. with crappier graphics, way more realism, and way higher unit counts. gives you the option to command the entire battle from yr general's perspective, sending out orders to yr subordinates through couriers. on matrixgames I think) Strategic Command: Global Conflict (WWII turn based hex grid game that covers the entire globe. unfortunately only on battlefront.com I think) Combat Mission: Fortress Italy (batallion level turn based scenario-based WWII game. think company of heroes with more realism and no base building. after you give out orders, you click end turn, and both sides moves play out in real time. likewise, though, unfortunately only on battlefront.com I think) Wargame: European Escalation (I haven't actually played this one because the specs are too high for my shitty laptop, but someone on somethingawful is doing a let's play of it that looks awesome, and one of my steam friends said it was the best wargame in ages. so check it out. on steam. Unity of Command (really good, and really hard, turn based hex grid game set on the eastern front of WWII. models supply lines and blitzkrieg tactics, among other things. easy to get into, really hard to master. available on steam) Darkest Hour (basically an updated/modernised version of Hearts of Iron II, the classic WWII grand strategy game. this one has a WWI scenario included. also there's an alternate history mod called Kaisserreich which s fun. on steam.)