Mercenaries: Playground of Destruction.
As soon as I read the manual for the game I was already immersed in the world. I actually felt like I was a mercenary in a war-torn country with various factions fighting for their own benefit and goals. The political connections the characters have were all interesting and all of the back-story concerning the build up to the war were all nice additions that added to the immersion.
Also the way the game handles contracts made me think about who I should ally myself with, who I should be wary of and how I would approach the factions. When going out on contracts you have to make tactical decisions on how you're going to proceed and take all things into consideration including; the existence of AA, possible civilian casualties, enemy placement, enemy armour and aerial support and of course the tools at your disposal.
I have had hour long gaming sessions where I played this game without saving once and just playing continuously, not to mention how many times I have played through the game just to approach everything differently and to hear the dialogue again.
Fallout: New Vegas
I actually cared about the world and the people in it enough to come up with my own opinion of nearly every major character and faction along with their various plights. When it came down to the final decision it actually took me a while to think, and then eventually after playing through all DLCs I was able to finally come to a decision about who I think would suit the Mojave the best and how they would go about it.
Dynasty Tactics 2.
I spend way too much time in this game simply looking for civilians to recruit, upgrading my officers with tactics and items, recruiting more officers, learning new tactics, recruiting officers, seeking out mystics, recruiting officers, creating new armies and forming defensive/offensive lines, recruiting officers, thinking of new tactic combinations and of course recruiting officers.
Damn I love recruiting people in Dynasty Tactics 2.