RAID-6 is the canonical answer, because it can handle *exactly* two disk failures. However, to cover your larger question, RAID1 can (maybe) handle two disk failures -- technically, an N disk RAID-1 array can handle N-1 failures, so whether a given RAID-1 will handle two failures depends on your configuration.

RAID-10 (or RAID-01, depending on your proclivities) can handle anywhere between M-1 and N/M failures (where N is the number of disks in the array, and M is the number of mirrors), depending on which disks happen to fail. If the M disks that fail are all the mirrors of the same data, then you're toast. On the other hand, if the N/M disks that fail are all mirrors of different data, you're OK. I'll leave the probabalistic analysis of what the chances of catastrophic failure for given values of N and M for you to do if you're so interested.