I try to beat a game before I buy a new one, but I'm terrible at this.  If I ever see a game on sale or cheap on Amazon I pick it up because I don't want to miss the opportunity of getting it and its gotten so bad I got like 30+ games on my backlog and a lot of them are JRPGs that are 20-30+ hrs.  I've been trying to buy less games, but its hard when games like Tales of Xillia come out and I have to get it >.<.  So I'd say I get a new game every other week, I'm trying to lower it to once a month so I can actually finish the games on my backlog.

I will sometimes buy a lot of games in a short time, or sometimes go while without purchasing a single game.

Once a month.
And I know exactly what you mean, it's hard not to buy sometimes :p

If not every week every two weeks. This week I purchased a few older games like NFS and LBP for Vita, the week before Dragon's Crown, and the week before that Ni No Kuni. And yes, my backlog is a behemoth.

Most of the time once a month, I buy quite a lot of games day one

In average once a month i'd say, but i definitly buy more than twelve. I guess its more accurate to say: New games i buy an aproximate number of 12 a year. Usually less than that, but then i buy quite a few discounted ones aswell.

Since July of this year i have one game buy planned per month until the end of the year. After that we dont have firm release dates.

i tend to buy in spurts but on average about 1 a week between all systems. i'm terrible about not finishing games too.

when im interested

Not counting the Steam games I bought in summer sale (about 10 euro).
A game every two months/quarter. I've only bought two games this year. It goes up though in the other half of the year.

Once a month. New games only around once every 3 months.