I never used to have this problem, but around a year ago I hit a wall. Almost 30 games installed and I couldn't bring myself to play any of them. So I spent some time trying to figure out WHY this was the case and I came to 2 conclusions.
1) The ME3 ending put me in a mild depression in general for about 3 months. I don't know why because I've never even played the first one and only played ME2 maybe 3 times, so I wasn't uber-attached to the series. And I felt nothing for shepherd dying, that was fine, hell even expected. I guess mostly I just wish there had been more space combat. As in any at all. I fully expected to play as Joker and pilot the Normandy third-person and blow up some reapers first-hand. I still wish that would've happened.
2) Partially because of ME3 and part just from looking down the list of what I have installed, I realized something: nothing has a Skirmish mode any more. Back when I first started gaming (I'm gonna say around 1997 or so) I played RTS games almost exclusively, and they ALL had a skirmish mode. Hell, the only game I had for the first 2 years on a PC was Command & Conquer: Red Alert and I didn't play a single online match OR any of the story missions until 2 years ago. I played nothing but Skirmish. When I got into Unreal Tournament, same thing. I used to spend hours with a redeemer in camera mode just nuking the fuck out of everything. And it was fun.
So I reinstalled C&C3: Kane's Wrath, Red Alert 3, and Supreme Commander: Forged Alliance, along with Unreal Tournament 3, and guess what? I don't hit burnout any more. I still play a TON of story games, but when the story gets too much, I fire up one of my new-old-favorites in Skirmish mode and focus on the gameplay and the tactics and just ignore the story. I do that for a day, and I'm craving for good narrative again.