I heard that using RAID5 or RAID6 can be problematic: if RAID controller stops working, there is too much pain to recover the data when you do not have another controller of the same type.
Now, is it the same thing with RAID1? Or in RAID1, everything is pretty easy, and if something breaks, I just remove one of n hard drives, and recreate a new RAID from this disk?
The problem for all hardware RAID controllers is the meta-data they stash on the drives themselves to inform the card how the RAID is configured. RAID1 is no less vulnerable to this kind of fault. The data is probably more recoverable, though even that depends on the RAID card in question. Long standing RAID lines like those sold by HP, Dell, and Adaptec tend to be pretty stable in terms of metadata formats so they're less vulnerable to this kind of fault.
I've had little luck re-creating a RAID1 array with a single member that the RAID card doesn't recognize as belonging to a RAID1 set. The RAID cards I've worked with have scrubbed the drives before putting them into a mirror set, which is a destructive operation.