Currently Online 
Ha!
Like infinite time on RollerCoaster Tycoon 2 and SimCity 4 since I've been playing them pretty much continuesly since they both came out twelve years ago.
No way to know, but it's got to be many thousands of hours. Likely even over several tens-of-thousands of hours a piece and I'm not even exaggerating.
Another contender is Anno 1602, but that probably wouldn't beat the other two. It's half a decade older than both and I played it a lot as well, but it been some time now since I played it and I doubt I ever played it more consistently than RCT2 and SC4. Still an easy couple thousand hours. Fourth would likely be Star Wars Galactic Battlegrounds, which I used to play a lot of multiplayer, I wouldn't be surprised if that game also easily exceeds a thousand hours. After that probably Medieval: Total War and Rome: Total War, which should both hover around the number.
For games that actually count time, it's probably Empire: Total War at about 200 hours. Otherwise it's Star Wars Knights of the Old Republic, I beat the game four times averaging 50 hours (the longest was a little over 60) a playthrough to also come to around 200 hours total which I'm pretty sure makes it my most played story-based game. Since time-keeping is relatively a newer thing, I don't have that many games that counted time and definitely not many games that actually lend themselves to playing for such lenghty stretches of time.
