Here's one from Stefanie...
Let's begin by saying that ANY medication or treatment can have complications. Go pick up any over-the-counter medication in your medicine cabinet and read the small-print. I'll bet you never realized how potentially dangerous aspirin and cold medicine can be. If you want a real scare, go onto WebMD and put in any symptoms you might feel every week. You may come out of that thinking that you need to update your will.
My point in bringing this up is that most of the anti-vaccine people quickly point to death and other serious complications of vaccines. However, the actual incident rate of such things is very small. On average a serious side-effect happens less than 1 in 10,000 times, so a dog or cat has less than a 0.1% chance of a significant reaction. Can bad things happen? Absolutely. But they are the exception rather than the rule and vaccines are overall considered very safe for the majority of patients, as well as being far better than the diseases we're trying to prevent.
In my 15 years in practice I have given countless thousands of doses of vaccines. Figure that I see around 100 patients per week and half or more of those receive vaccines. A little quick math...50 work weeks in a year...2500 x 15...so I've given somewhere around at least 35-40,000 vaccines so far in my career. Out of all of those I've seen 4-5 truly anaphylactic reactions that almost resulted in death. More common reactions are vomiting, facial swelling, and hives, but even those happen less than 10 times per year (still great odds) and are normally just uncomfortable without being life-threatening. Being sore, lethargic, or running a low-grade fever are all normal for a day or two after vaccines and are not considered "reactions", instead being "responses" that are normal for the immune system. With proper precautions such as pre-treating with antihistamines or antiinflammatories, these mild reactions can be prevented. In fact, one of my own dogs had facial swelling after her first adult vaccines, but I continue to vaccinate her with no problems by giving her diphenhydramine injections before and after the vaccines.
So what about the meningoencephalitis that Stefanine mentioned? This is a serious inflammation of the tissues surrounding the brain and doesn't show up immediately after the vaccine. It seems to happen more commonly in very young dogs that are given a modified-live vaccine, while rabies are killed vaccines. In fact, in my searching it seems to be more common after a distemper vaccine than any others. That being said, it's probably the rarest of all vaccine reactions. I've never seen one in my career and have never talked to any colleagues who have mentioned this. It's certainly nothing I ever worry about in my patients or my own pets.
Most of the time you'll see effects like this one and others brought up by people who are against vaccines and are into holistic or homeopathic therapies. Yes, they can show incidents of such problems, but they are overwhelmingly the minority of cases and are statistically rare. They are also impossible to predict ahead of time. Make your own decisions but realize that most vets continue to use vaccines on their own pets without concern.