well for light gaming you get a lot of value for your money, but don't expect anything amazing. For a couple bucks more you can get the Athlon II X3, which is very good for gaming. I have built numerous machines with it and for a chip which we pick up for 33BD here it is nothing short of amazing.
Not to mention, a lot (60% I believe) of Athlon II X3's can safely have the 4th core unlocked stable, and boom, for the price of a dirt cheap cpu, cheaper than an i3, you have a beautiful quad core cpu!
A faster Athlon II X2 like the 260 can probably manage a "passable" job with many games. If you are building a system yourself, however, another $20 or so (here in the USA) buys a Phenom II X3 740BE, a significantly better chip (although you'll also need to buy a $20-$30 HSF for it). If you are NOT building this system yourself, carefully check for what chip it is. Some low-end machines are being offered with the Athlon II X2 240e and 210e. These are the slower, low power versions, which are fine for Internet surfing and email, but would be unsatisfactory probably even for Flash games.
Edit: The 740BE also has a reputation for unlocking easily to a X4; mine did just by changing one setting in my ASRock board's BIOS.
Many AMD mobo's these days are advertised to have a "Core unlocker" feature.
In fact, my new mobo I got a few days ago has a little flick-switch at the very bottom labelled "Core Unlocker", and when I go through BIOS it tells me to click "4" during the post to start core unlocker.
I don't use it on my rig though since im running a 965, which doesn't have any locked cores.