I have two cats.
About 7 years ago (I was just out of college) we went in for annual visits for our cats and the older cat was given 3 or 4 vaccines - rabies, distemper, something for a cold kind of thing, and also feline leukemia? I think? The younger one was just a baby and I think she got one or two, but I can't remember. Anyway, I just got all the shots the vet suggested. He had had a really rough visit, too (he's not good with being able to smell the other animals and *really* not good about letting people touch him) and was held down and masked and he peed on the table - and all that just so they could listen to his heart! It was horrific for all of us. My cat was sick for about a month afterward and I really thought I was going to lose him. He had a fever and stopped eating or drinking and pretty much just hid in this one place. I ended up giving him kitten colostrum in a dropper to get him back to health. We thought it was from the stress of the visit, but now knowing more about vaccines, I think it may well have been a vaccine reaction.
We decided after that to stop bringing him into the vet unless it was desperately necessary. Both cats are indoor only. This year, though, we found a vet that does home visits exclusively

: which has been GREAT - the cat had started having some problems (turns out it's a thyroid issue), and we called this home-care vet and he came over and was able to examine the cat without all the trauma and was even able to fairly easily get a blood sample! (so exciting!!) Anyway... we told him why we stopped taking the cat to the vet and he looked completely dumbfounded, but has yet to mention any vaccinations to us, so I wonder if he thinks that's what it was, too. It's been 7 years or so since the cat had been to a vet, so he was clearly "due" for vaccines.
Anyway, that's our story. I'm not that worried about most of the diseases b/c the cats are indoor only and we don't board them or anything.