Depends on what you edit. Single track or 10+ tracks, If you can live with slower performance, some occasional jerkiness, then no, you don't NEED a raid, but it makes for a more fluid and nicer editing experience if you do have a good raid.
AVCHD/XDCam prefered yes but more than 2 sets raid 0 does nothing for it..
Red 4k or uncompressed big dog 8 + drive raid array
For most camera formats, including AVCHD, you will not need a RAID. Any modern hard drive will be more than fast enough for multiple streams. (Unless you normally go up to 10 at a time as Harm suggests. But even then, your CPU is likely to cause playback stutters before your hard drive does.)