well, that was quick

Newbie question - unless a donator explicitly sends me an email stating that they've deposited some BTC, is there any way for me to identify and "thank" them on my website? it seems not?
Rich
Unless they use the one and same sending address every time (most people don't, on the contrary), and unless this sending address is publicly known and verified to belong to that person - no. (Some publicly identified addresses are tagged on blockchain.info).
Importantly, even if someone emailed you claiming to have sent a particular donation, that doesn't mean they did. Anyone can see all the transactions, as Bitcoin ledger (a.k.a. blockchain) is public.
One way to verify is to ask this person to sign a specified message using the private key related to the sending address (or one of the sending addresses) - you can then check this digital signature. Bitcoin.org client offers this functionality.