If you want to store a lot of data, RAID 5 or 6 is a really good way to do it if you do it correctly and understand the advantages and risks.
To begin with, I want to address the claim that you need to use expensive RAID cards otherwise RAID is "slow". This is absolutely not the case. Parity calculation on large arrays is very intensive. Cheaper RAID cards and software RAID offload the calculation to the driver, which runs most or all of the parity calculations on the CPU. Good RAID cards, on the other hand, which typically cost in the hundreds if not thousands of dollars, have their own chips for calculating the parity.
For Enterprise operations where arrays might be serving hundreds of terabytes an hour, offloading the parity calculation to hardware is worth the money. For home users, perhaps not so much. What you should realize is that without the expensive hardware RAID, writing to an array can slow down your CPU. If you are building a home server this might be acceptable. If you are running RAID on a gaming computer, this might effect your games. However, keep in mind that parity only becomes CPU intensive during writes, not reads. Reading from a RAID array is generally much faster than from a single hard drive.
Now, as for the question of rebuilding a RAID array causing data loss. You have to ask yourself a few questions:
1) How important is my data?
2) Am I going to back it up, such as to tape?
3) How many drives do I want to use?
4) How much money do I want to spend?
For home users, in my opinion, the biggest chance of data loss comes from not a HDD failure but a controller failure. If the controller fails and you do not have a spare and cannot find that exact model, you might not be able to recover your data. It might actually be worth it to use a slower software solution, like one built into windows server, because then the RAID is handled by a fairly universal OS instead of a proprietary driver and hardware controller.
Now, when a RAID array fails and you are rebuilding the array there is a chance of losing your data. This can happen if one of your remaining drive fails or if there were undetected bad sectors in the wrong spots. Both of these are rare, but they do happen. If you are not using a second backup system (such as a tape), your best bet is to:
1) Reduce the numbers of disks in your RAID array. The number of disks increases the probability of a failure during rebuilding geometrically. For RAID 5, you should never use more than six disks. I would recommend sticking to five. Rebuilding stresses the disks and increases the probability of failure.
2) USE RAID 6. RAID six has tolerance for two disk failures, but requires an extra disk for parity calculations. If I remember correctly, a six disk RAID 6 only stores as much data as a five disk RAID 5, but your chances of two disk failures during rebuilding is geometrically lower than a single disk failure. RAID 6 is generally viewed as pretty data-loss proof during small array rebuilding.
The TLDR summary:
My advice is:
1) If you don't use an expensive controller card, only use RAID 5/6 on a home server so as not to slow down your main computer. If you do use a controller card, get a backup card in case the primary one fails.
2) Either backup your RAID or use RAID 6.
3) Do not exceed 5 disks for RAID 5 or 6 disks for RAID 6.
4) Have a spare disk handy so you can rebuild immediately.
5) Remember, RAID was not designed for backup. It was designed so that you can keep critical data available without any downtime. If you use RAID 6 with a small array and rebuild any failed drives immediately, your data is probably pretty safe, but if you just slap together a RAID 5 array and assume your data is safe, it might end up being a nightmare for you. RAID data recovery is very, very expensive, usually several thousand dollars.