I use RAID 10 with hardware RAID cards (Adaptec 6805E) with Supermicro 5-in-3 hotswap enclosures. I could also configure a hot spare, which the controller would automatically spin up and rebuild to in the event of a failure, with no user intervention needed.
If a drive fails, the hardware card makes an earsplitting alarm noise. If the hotswap enclosure fan fails or starts to overheat, the enclosure makes an earsplitting alarm noise and flashes red lights. You can also configure the RAID software to notify you by email of any problem.
I use RAID 10 because it is simple, has fast write performance and excellent fault tolerance. A RAID 10 array can withstand multiple drive failures, and rebuilds only take a few hours (no parity to calculate). RAID 10 is also ideal for working files (like a photographers) because it has high write speeds. Decent write performance on RAID 5 or 6 requires a battery backed cache, and such controllers are far more expensive than the entry-level RAID 10/1/0/1E capable controllers. I think RAID 5 should be avoided, and that RAID 6 only makes sense for dedicated file servers.
I would recommend a hardware controller over Intel's built in RAID. Intel RST isn't bad, but it is far slower in my experience. With a hardware controller you can move the whole array to another machine in the event of a failure, all the functions are OS independent, and you get perks like onboard failure alarms and much higher quality SFF-8087 cable connectors.
RAID is not backup, of course. I use Crashplan to perform cloud backup of my most important data.