As a general rule larger corporations are willing and able to sponsor H1B and F1 visas for non-US citizens living and working in the US. It is more difficult for companies to bring people in from outside the US however. It is generally on a case by case basis which companies require US citizens or greencard holders, and which will sponsor visas.
We are actively placing TopCoder members at clients, and if you (or anyone else) is intersted in employment opportunities, but needs a sponsor for a visa, right now, UBS and VeriSign, TCO sponsors, would be your best bet. They are both actively pusuing TC members, and they have many great opportunities available.