Worst reaction I've ever had was to strangles IM vaccine. My now senior half-arab gelding would get golf-ball to tennis ball sized swelling at the injection site. While I was boarding my horses, it was a required shot, so he had to have bute for 5 days around the injection (2 days before, day of, 2 days after). Now, that I no longer board, none of my horses get the strangles vaccine (if I ever have to again, we'll try the internasal kind).
My APHA mare had a mild reaction to WNV vaccine last year (3 year on the vaccine), very small localized swelling at injection site.
Can't recall any other reactions in the 20 years I've had horses.