Being a US based pilot, and gone to Canada a few times, I'll offer my take on everything. (Granted I've never done this with animals).
Chris hit the biggest parts of crossing the border, with the new eAPIS filing requirements for all passengers/crew aboard a plane. This is basically advanced notice of immigration declaration and allows everything to be checked prior to departure/arrival. This needs to be filed for BOTH legs of the trip (departing USA, and arriving back into USA). AOPA Air Safety Foundation has a great tutorial about eAPIS and how to use it, register it, etc: AOPA ASF Tutorial
USA pilots need to have a passport, airman's certificate, valid medical, and a Restricted Radiotelephone Operators Permit (issued by the USA FCC). To be perfectly honest, I've never been asked for the radio permit, and I've never heard anyone who has, but I wouldn't suggest crossing the border without it just in case a USA CBP Officer isn't in a great mood.
Passengers need to have a passport.
Aircraft need to have a *permanent* registration, no pink slips here. All the normal requirements apply (POH, W&B, etc...). Older planes might have an issue if your tail number (N-Number) is smaller than 12" in height. At the club I rent from, this has limited 2 of the planes as we still have the old 3" markings on them. Also you need a Mode-S transponder (shouldn't be an issue for most pilots here). The requirements for LSA & Experimental aircraft are different, and I don't fly either, so I wont try to guess.
USA CBP requires that incoming aircraft have a User-Fee Decal attached to the plane. Each one is $27.50 and is good for a year.
Landing Requirements: You must land at an Airport Of Entry both in Canada and in the US. I've flown into Windsor, ON (CYQG) in Canada, and came back into Midway Intl, IL (KMDW). Canada CBSA (link)
is super nice, and they don't really give you much grief. You call them before you depart, and right when you land. They typically just clear you over the phone. USA CBP is a bit different, (link)
. Landing at a User Fee Airport is hella-expensive, which is why we've gone into MDW (international airports have USA CBP on-staff). The officers range from nice to annoying-power-trip, just as if you go through normal immigration/customs... Again, they need notice before you leave (be accurate with ETA!).
As far as customs go, both countries have been a non-issue (it's always just been me, a few buddies, and a backpack). I'd check all the requirements for dogs though with Canada's Food Inspection Agency (CFIA Link)
(they cover pet imports).
Additionally, make sure you're on a VFR ADIZ/IFR flight plan
before crossing the border. Don't want another scare with the jets being scrambled like what happened to that kid a few months back.
By the way, be prepared for a little bill from Canada with User Fee's.
Even the 10 nm it takes to go from Detroit to Windsor, I've gotten a bill for like $20. Everything I've gone over can be found on AOPA's excellent guide: International Flying - AOPA
Don't take my word for it, go visit them!
Hope that helps.