If you are hosting on a server(as everyone is) it will, at some point fail. You have to choose a service that has minimal failure combined with quick resolution times. I think AWS fits this description...
AWS has had far more failures than my servers at any data center ever have. Running in 'the cloud', you're taking all the unavoidable points of failure (power, network, hardware) and adding in a bunch of proprietary ones (all the software that manages EC2, EBS, ELBs, internal routing between them, etc) that have all failed spectacularly at least once already with hours- to days-long resolution times.
Yes, risk still exists, and risk profile shifts a little, but I find it to be a toward the better. Here's an anecdote:
I run applications on EC2 and RDS. I'm using Oracle. AWS has recently introduce Multi-AZ Oracle, but I haven't enabled yet. Before it was available, though, I set up a poor-man's procedure that consists of running data exports and dropping them on S3.
Now, when everything went to hell in the east, I lost an RDS instance. I couldn't do point-in-time restore, and I couldn't snapshot (both are still pending since 7 AM or so).
Luckily, I was able to spin up an RDS instance in the west, pull down the latest data from S3, and do an import. I repointed my apps at the new database, and now I'm back up.
The process took about 45 minutes. Setting up the backup scripts took about 20 minutes about 2 years ago. Now I'm just sitting on my hands waiting for the AWS ops team to fix everything. This is work I'd normally be scrambling to do myself. I'm quite happy to let those talented folks deal with it. When it's all back up and running, I'll check integrity and consistency, and I might have to restore some interim data, but for now I'm operational.
I'm sure there are worse scenarios, but the major outage last year and in the past 24-hours were quite easily mitigated.
There's something to be said for being part of a giant machine. AWS really is utility computing, so even the small guys get the benefit by virtue of standing next to the big guys.