TL;DR; Yes they're trustworthy, generally speaking
Edit: I see we might be exceptions. We have been using OVH since 2005, running up to 40 servers about 2 years ago. We are also running at iWeb, Softlayer, Amazon and Leaseweb. Hardware wise the only one we have issues with is OVH, and i'm talking every 2 weeks since 2005 (in 2006 they managed to lose all our data on 2 clustered RAID machines; one died, all corrupted, then when we were busy setting up the replacement, the other one died...). But they are so cheap and easy (like the easy OS installation which is cloud-like, already for many years) we stick with them for some projects which need high spec hardware in clusters. Note: the SSD drives are great, no problems with those so far (knock on wood).
They also do remarkably well: out of the thousands I've had from Leaseweb and OVH, OVH wins hands down.
I sort of wish hosting companies would publish the hardware failure rates -as seen by them- too - though I don't know how much of a competitive advantage that would be, if any.
I'm kind of wondering now if we are running different workloads; we are running very high IO and network stuff. Maybe we just hammer a lot harder on the disk than others are? With HP DL360s @ leaseweb we are running the same loads without any problem (since 2006...); 1 broken disk that ended up not actually being broken.
Of course, if you're working on a larger project with enough budget, services like Akamai provide methods of routing your static content via their network, further reducing the problem.