Usually I'll bring home something special, some sort of treat for the birthday pet. It might be something they need, like a new bed, or just something fun like a new toy.
We once had a dog birthday party for our old Aussie. She was turning 2 and I was 6 so I thought she needed a birthday part. We had a few dogs that we knew VERY well and dogs that Lady knew also. We only had 3 come, so it was a manageable number. We had a real cake for the people and gifts for Lady. It was fun.
This year, on June 2 J.C. turns one and on June 3, Holly turns one. We might throw them a special party... sort of an excuse for us to have birthday cake and to pamper to dogs and then make them wear a ridiculous party hat for a picture.