I generally don't burn out. Instead, I feel something a bit different, especially playing games which take a long time to complete. I rarely play multiple games at a time, which I'm sure is a factor, but that's just how I game.
Generally, when I finish a game, I get what I call the "Gaming Blues", which makes it hard to start another game right after another. Most of this is likely due to having to "relearn" to play another game given controls are different, as well as game play.
I got lucky with Oblivion, which took me to Skyrim, then to Fallout 3 and New Vegas. Because the controls were virtually identical, there wasn't much lost between games. It took me a long time to get into a new game afterward, though, because those games did such a damn good job in controls that it set the bar for other games (at least to me).
The other time I get distraught is when new consoles come out, like the current gen systems. I try to focus on moving to the new console, but these games have been totally horrendous. So far, I've yet to find one worth the AAA money. The best game I've played on the XBox One was Max and the Curse of Brotherhood.
In looking at what's coming out... I think I was too stupid to get this console this early, but at the time of purchase, I got it for a great deal (less than $300) once I traded in my Wii (that I rarely touched).
*sigh*
I miss the Gamecube. Don't get me wrong, I love the 360, but there's no denying the power of Nintendo games and the fun they bring. These "hardcoe" consoles lack these simple but fun titles.