Me and my [older] brother have identical music tastes, so I usually just rip songs from borrowed CDs so I can more easily listen to them on my computer, and also so that I don't have to open the DVD drive, put in a disc, listen for 15-20 minutes, open the DVD drive, find another CD, etc, etc, etc. It's also more convenient for when the drive is occupied with a game disc.
Anyway, before going off topic too much, the first album I remember buying myself was about a year ago and was Radiohead's In Rainbows via digital download from their website. I haven't actually bought my own album since, and the only reason I bought that was because it would have saved me the effort of ripping my brother's inevitable CD purchase a few weeks later.