Can I ignore 1099s for non-U.S. residents/entities? We have brought on some service providers in India and the UK this past year.
You can read the particular dos and don'ts right here on the 1099 form instructions courtesy of the IRS: http://www.irs.gov/pub/irs-pdf/i1099msc.pdf. However, they are not specific about foreign entities on that form. However, in the U.S. you only issue 1099s to non-corporate entities (contractors, consultants, some LLPs and similar entities - read the specifics on the form) that are U.S. entities. So you don't have to complete 1099s for non-U.S. residents.
If you are a U.S. company or an individual paying a non-U.S. person (non-citizen and non-tax resident) for services performed outside the U.S., then you will likely need one of the Form W-8s, likely a W-8BEN, to keep on file to support the amount of withholding, which could be zero. I don't think a 1099 would be appropriate. I'd be happy to discuss further if you would like.
I would modify that a bit to distinguish between US taxpayer non-residents and those who are not US taxpayers. If you have a consultant who is a US citizen or green card holder who happens to live abroad, I think that person should also receive a 1099-misc. The question to ask might be whether the person/entity you are paying has a US taxpayer ID (SSN or FEIN), which gets to the heart of it as a business question rather than a personal question.