Just hire people as contractors and it is extremely easy. They send you invoices periodically, you send them money through regular bank wire transfer.
Of course, making this kind of thing not worth your while is the whole point of protectionism. IIRC, India has a similar arrangement.
One way around this is presumably to open a branch office in another country, and have contractors work for the branch.
That can't be true for contractors, or sites like Elance and oDesk would not be able to operate as easily as they do. A contractor is responsible for paying his own taxes, whether that is to the IRS in the US, or the tax authority in his own country.
You proved my point:
Foreign persons are subject to U.S. income includes: tax at a 30% rate on income they receive from U.S.
http://www.irs.gov/pub/irs-pdf/iw8ben.pdf
The burden is on the foreign person, not the US company. The US company can pay you as a contractor and not withhold any tax (just as they could with a US citizen 1099 contractor). The foreign contractor would have to file the W-8BEN (or not, since the US likely can't prosecute offenders in their home country).
In any case, the whole thing is a pretty arduous procedure in international comparison.
[1] http://www.irs.gov/publications/p515/ar02.html#en_US_2013_pu...
The offshore bit was pointed out to me recently and so I had to set up a proper European Union company in a hurry. Now all is well.
It's easy to subcontract work out to other countries if you're not tied to the idea of having employees, but instead hire companies (companies which already exist, like say small design shops, packaging firms for apps, or tech firms) to perform services for you, rather than individuals.
Take 37 signals for example, when they were a consulting company. A company in say Paris could have hired them to work remotely, without worrying about paying income tax - that's all handled on the subcontractor end if it is a company.
I could also imagine a kind of "talent agency" model, though that doesn't seem to have caught on in tech. (Yet? I'd sign up for that if it provided me with a steady-ish flow of high-quality gigs and sorted out all the legal/tax paperwork for me.)
Back on topic, that's exactly what the original commenter (zura) suggested. You can hire a foreign company for contract work without needing to hand over an entire project - you'll be paying for deliverables/features instead of time, but the end result is the same. AFAIK you have to report it to the IRS, but don't owe any taxes on it.
(Edit: I see ljoshua beat me to the possibility for issues here but it's important to emphasize that it can be done, just play by the rules to avoid trouble down the line.)
[1] http://www.irs.gov/Businesses/Small-Businesses-%26-Self-Empl...
EDIT: Employees also don't want their home country's protections in case that company in Uzbekistan decides not to pay them.