Contrary to popular belief, you don't normally need any special privileges to debug programs on Windows. If you start a process, you own it and thus have full permissions to it. That's all a debugger needs. However, if you want to debug processes running in other logon sessions (services, for instance, or IIS worker processes) you'll need the Debug privilege. This privilege allows you (and therefore your debugger) to open any process on the machine for full permissions, even operating system services. It's a really powerful privilege normally granted to the local Administrators group, so instead of granting this to my account I simply start the debugger from my admin prompt (if you've set up your environment like I do for .NET, you can just type devenv to get it started).
If you're running Visual Studio .NET, you must add your low-privilege developer account to the local Debugger Users group. This is not an operating system requirement, rather it's a policy enforced by Visual Studio .NET. If you aren't a member of this group, you aren't allowed to do JIT debugging, remote debugging, or pretty much debugging of any kind using Visual Studio .NET.