As safe as any other major web site or hosting service. Transactions to the back end of the EC2 are conducted over SSL, which is reasonably secure. Amazon's back end has proven quite safe so far; there are no reports of leaks. And given how many credit cards are stored there, and how much money moves through it, if there were security leaks they'd have been found by now.

Once set up, an EC2 virtual machine acts just like any other machine on the Internet. It's largely up to you to ensure that the applications you run on it are secure. It doesn't matter if the computer itself is completely secure if your application isn't set up properly. There is an operating system running on each instance, so you're subject to the security issues in the OS, but Amazon is keeping those instances patched and up to date. So if you're running Windows, it's as secure as any Windows installation on the Internet. Which is not as secure as you might like, but it's no less secure just because it's on EC2. You can also get Linux, in any of several flavors, with the same level of confidence.

In other words, unless you're a security expert, an EC2 instance is likely to be at least as secure as a computer you're running yourself or an application server rented from any other hosting company. While I wouldn't run a nuclear power plant or air traffic control system on the EC2, it's going to be secure enough for pretty much any ordinary application.