How much slower is RAID 1 than no RAID at all? I have heard that RAID 1 provides peace of mind (because of mirroring) but gives slower write (not read) performance.
Depends whether you are dealing with hardware RAID or software RAID and what the circumstances are (e.g. controller being used, controller memory, buffer sizes).
Generally you will see a performance hit using software RAID. With a decent hardware RAID controller, depending on the sizes of files being written, you will see little to no difference as the files can be buffered into controller memory then written at a later time.