For general computing purposes, i.e. surfing the net, using email, using apps like Office, Pages, and Acrobat viewer, 512 RAM is plenty with any OS.
If you work with occasional video files, small to medium (under 2000) iPhoto collections and play games for fun, nut for the bleeding edge framerates, then 512 will work fine as well.
If you do any amount of video editing beyond that of hobby work, have large iPhoto collections, play hardcore FPS games, work with images in Photoshop, large sound files, etc. Then RAM is your friend.
In general, OS X tends to be decent with RAM. You can actually run Jaguar with 128 on a 300 mhz G3 and use mail and surf and not have it been painful. (its slow no doubt, but not slit your throat slow). So, 512 will suit the average home user just fine. From the developer demo of Tiger (I work at a University and Apple did a demo last week to prepare us for the migration) the machine he used was 256 megs. For most of our campus machines, that is the norm, and it was quite responsive for web activities, email, wordprocessing. So I can say firsthand that on eMac 1 gig machines with 256 RAM Tiger is as fast as Panther is.
Unless you are a poweruser of some sort, 512 should last you with this OS update. The most limiting factor for you is the GPU. Your mini has an underpowered graphics system that will not take full advantage of core video, and the latest Open GL games, etc.