Rented in the Caribbean, parts of Europe and the UK. If you are staying for more than a few days, generally, renting becomes cost efficient (e.g. I'm looking back at the Shetland islands for a holiday without the Do next year - a hotel is approx £100/night, so £700 for a week - I can get a self catering cottage sleeping four for £350 - £400/week!
I've rented through agencies, and directly from owners. If directly, I want to see a record elsewhere than the owners website of other people commenting on staying at the villa, or of agencies also offering the same property. But, if I find a property with an agency, I'll also check that I can't rent it directly, to save the agency mark-up...