I never get bored of Fighting games, First-person shooters, Third-person shooters, or pretty much anything not Turn-based. I only seem to get bored of games that are Turn-Based, it's weird because Pokemon is half turned-based and I play it all the time and it's the only turn-based game that I enjoy. All other ones I quit 5-10 mins into them. I guess I just don't have the patience to play those type of games.
I'm never bored of any genre as long as it's done right.
With the exception of games like guitar hero or DDR, where it becomes a game of memory rather than reaction. If the arrows were random that'd be a whole other story.