Well I guess you should rent the game first to see if it's something you're willing to spend a lot of money on. But Since I don't do that I just buy the game.
I think it comes down to which game it is, if it's a good game and well know of course I would buy it but if I've never heard of that game before I would rent it and test it out.
In my country you can't rent games (in most places) so all you can do is buy it and look if it's rubbish or not. I usually make sure to look at reviews before purchasing games.
I almost always buy games these days because renting games is expensive,(I don't like the online game sites) and I haevily research a game before I go a buy it.
i used to rent ALL THE TIME as a kid and never bought unless its a sequel to a game i already owned and loved but nowadays i just buy the games taking the risk it might suck the only time i rent games is if i wanna try the same game on another console (like i do i have black ops on ps3 but wanna try it on the wii)
Buy good games that i know i'll love (usualy games for consoles like WII or great series like AC, spore, etc), occasionaly I lend/borrow games wih friends so we can both try out some new games. I also download some games but those are ussualy games I either already have (but for some reason they don't work, or when i want to play without CD's) or games that are prety old and hard to still find in shops (and I'm not planning on spending 30-40 bucks on a used game that used to cost 5 bucks new but since they took it of the market it supposed to be limited edition) I realy don't see myself renting a game, you can usualy buy a decent (but older) game for the price of renting a new one If you're so desperate to try out a new game.
Renting has it's purpose's. Why waste a lot of money on a game that isn't good. So people rent the game first to see if it's something to drop a lot of cash on.
I buy games if I think I'll really get my money's worth. If I'm really on the fence about a game I'll rent it, this has saved me sixty bucks on more than one occasion. Also, I can't afford to buy every game I'd like to play so being able to rent games is nice for the ones I'd like to fiddle with but can't justify paying the full retail.