Legally, I believe (but am not a tax professional) that you need a receipt if your donation is $250 or more. Otherwise, I believe your canceled check is good enough.
Many rescues will send thank yous on any size donation or on donations over a certain amount. Oftentimes our donors don't send in addresses with their donations, but we can get them off your check.
Since many rescues are all volunteer run or primarily volunteer run, they might not get receipts out right away.
If you need a receipt and don't get one within 1-2 months, there's nothing wrong with writing the rescue and asking for one. I know we've had a couple of times where we've sent a receipt but it went astray in the mail somewhere...