After release? Usually years. I don't care about playing the latest and greatest, just about how good of a game there is, and by this point, there are an awful lot of good old games. And, I don't like spending tons of money on games, since I'm somewhat cheap, so I tend to wait till there's a good sale, which is rarely close to release.
I can think of four games that I have personally bought (paid for myself, not received as a gift) within a month of release:
- Civilization IV, in 2005. Bought a week after release for $40 (20% off), hard copy.
- Age of Empires III, in 2005. Bought a week after release, also for $40, 20% off, hard copy.
- Chivalry: Medieval Warfare, in 2012. Bought about a month after release, $10, 60% off, digital copy.
- Europa Universalis IV, preordered, 2013, $34, 15% off, digital copy.
For all except Chivalry, I'd already played the predecessor heavily, and it's only Civ4 that I wish I'd waited on. Chivalry was already pretty inexpensive when I bought it as part of a four-pack with friends. But as you can see, it's pretty infrequent that I buy a game near release.
For how often I buy a game, it depends on if you count buying multiple games at once buying once, or buying, say, five different games. It also varies a lot by how good sales are. Sometimes twice a week, sometimes once every two months. But I tend to wait for sales, since for all but the rare game I'm really looking forward to, I tend not to play them as soon as I buy them (another reason I tend not to buy soon after release - why pay full price if you're unlikely to play it right away anyway?). So I bought Gunpoint for $2.50 last week, but haven't played it yet (other than the demo a month or two ago, which convinced me to buy it) since 95% of my game time since then has been continuing EU4 games (and the other 5% has been my in-progress Half-Life: Blue Shift campaign).