raid0 is for performance. you'll get double performance by using block striping (in a sense kinda like dual channel ram) using 2 or more disk. the downside, if one of your disk is damage, it'll break raid array, and you'll lost ALL data. i never had any problem with it so far (and hopefuly not), never heard about it also. if you had bad sector, make sense, but that also apply on single non-raid hdd also.
if you don't want to move to SSD, this is a nice alternative for OS disk and apps/game. my raid raid0 config (2 wdc caviar blue) dan get me 230MB/s sequential reading. faster load time

not recommended for important data.
2x500GB raid0 => 1TB volume
raid1 is for realiability. baslicly you use extra disk to mirror your main disk, yes, you'll always have a backup of your files, therefor, when your disk is failing, you'll have an extra data backup. you might want to consider this, if you want a reliable storage for documents, or other important data. but not for OS, apps, or games
2x500GB raid1 => 500GB volume
depend on what you need, and the nature of those raid, you simply can't compare those 2 mode.
you can also combine raid0 and raid1, but you need atleast 4 disk
if you're really worried about raid0, just use small (say, 2x250GB for OS and apps/game) and get another extra disk for data (either single non-raid, or make it raid1)