Amazon Web Services
* Bitstamp is now running on Amazon’s world-class AWS cloud infrastructure, architected to be one of the most secure and reliable cloud computing environments available.
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My main quibble with them is that they tout EC2/AWS as secure. It is certainly reliable, it is certainly backed by a company that needs security, BUT, it is a virtual environment using Xen as the hypervisor. There have been security issues there and with paravirtual hosts in general. It is kind of like private keys - if you don't have the keys, you don't own the coins, here, if you don't have the servers, you should be concerned about security.
I do have a non-Bitcoin server there and have for about 8 years, but it is a web server not handling potentially millions of dollars and could be restored elsewhere quickly. It is quick, reliable, and not too expensive, but not rock bottom.
Much would depend on the architecture and multi-sig will sure help, but I would always worry about VPS when handling big money figures. Hopefully they worry about it too.
AWS does not necessarily imply EC2. They did also reference new physical hardware as well so one can infer that they keep their secrets to themselves (and, in some people's theory, their less-than-fully-trustworthy staff ) Even if it is EC2 that they are using, there are a ton of things one could use a VM for which don't involve super-sensitive information. Conversely, there are a lot of services besides EC2 that one could pass sensitive info through if the design sucks.
I've used AWS for various things in the past, and very possibly will in the future. They are reliable, cheap, have got a large global footprint and are well peered. One needs to have a rational design to avoid any potential lose secrets, but that's just standard system design.