Two come to mind:

1. When I turned 14, my little cousin's funeral was the day before my birthday. She was only 5 months old and died from SIDS, and it was obviously extremely devastating for my family. I've dealt with a lot of death in my life, but I had just babysat her a few days before and it was the most shocking thing I'd ever experienced at the time. Understandably, most of that side of my family didn't acknowledge my birthday, and I don't blame them a bit.
2. My most recent birthday was even worse, but in a very different way. A lot was going on in my life, I was dealing with guilt from something majorly shitty I had done, and one of my best friends decided that was the day to say some things that I definitely didn't want to hear at that moment (at like 7 in the morning, so I got to think about it all day, LOL). I had a huge meltdown (I have BPD, which can cause some very quick, volatile mood swings), wrote a suicide note, and generally just felt like the world was falling apart. Now that I have some distance from it, I know it was mostly my disorder just running wild and I don't blame my friend for saying what they did; but it definitely goes down as one of the two worst birthdays in my life.