Just check on-line for each country's rules. I entered Brasil once on a passport that was expiring in 3 weeks. As long as the passport is valid the day you enter, you're fine.
One piece of advice on your passport renewal - always go to a Passport Agency office, if you live in a city with one. You get your passport in 3 days or less, and you don't have to worry about it getting lost in transit. This is particularly important for people who have visas, since at the Passport Agency, they just punch holes in your old passport to invalidate it and hand it right back to you when you submit paperwork for the renewal. I've known too many people who have had to redo visas when their old passport wasn't returned with their new one when using standard mailing or even FedEx for the mail-in processing.