Pretty much everything that has been mentioned already and a few more:
"Windows is now shutting down..."
After sitting for days. Good ol Win98, and the shutdown feature that never actually did shut down the computer.
Win98 in general I don't really miss. It is fun to play with it to get that Nostalgia feeling, but that lasts about 30 seconds. I really don't miss having to reinstall every 2 weeks because it was such an unstable system that crashed at random for no reason. BSODs were pretty much the norm. Now since 2k they are somewhat a thing of the past. If you do get one it's usually very bad, and usually has a somewhat decent reason, instead of it just being random. I remember the VXD error was a common one in win98.
I also don't miss dial up. Was a pain having to work on a computer that cannot be easily added to my network so I can transfer stuff from my server or what not. i still get dial-up computers occasionally, but it's rare now.
I remember IRQ conflicts, THOSE were nasty. I had one on my PC that took me like a month to figure out. It was a huge game of trial and error. I was also newer to computers then.
Remember when you actually had to use a boot disk to start a windows install? wow, I just remembered that now. That good ol win98 boot disk. I had made myself several copies of that, and had even customized it to my liking, like a custom logos.sys file so it shows a different picture when it booted. Oh, how fun this was. Come to think of it, I don't dig as deep into the system as I did then... I need to mess around with that stuff again, that's how I learned a lot about the internals of the OS.