An LLC is typically a pass-through tax entity. Those without tax IDs cannot receive income on a K-1. So, @Ross can own a C but not an S corp, for example. LLCs are often organized as pass-throughs, though I don't know if that's true in every state (in the US, you organize first in a state, then register at the federal level for a corporate tax ID. I'm familiar with the incorporation laws of a few states, but definitely not all 50; so maybe you can have an LLC that's not a pass-through in some cases).
Delaware is a popular choice to register in, but other states can be fine too. Make sure you pick a state that's easy to work with unless there's a specific reason you need to incorporate in one state in particular.
As mentioned above, CTCorp is a reasonable choice to sort out annual filing requirements for you. You do need the annual services of someone in the US to take care of providing a physical address and filing paperwork for you.
Generally speaking, people without tax IDs (example: Social Security Number) are at a tax disadvantage, as they'll be taxed twice - the corporation will be taxed, and then they will be taxed by their local government when receiving income as dividends rather than K-1 disbursement. This is the only restriction though - otherwise citizenship and geographic location of the owners do not matter.