I'm sure it's a guy thing, but the thing that annoys me most about moving is the electronic stuff. There are so many things that need to be connected with a bunch of wires, and you have to take at least some care in disconnecting it all before you wire it all back up after the move. It's incredibly annoying. Particularly if you have movers, they can easily just pack everything in your underwear drawer, and you pull it out at the destination and put it back. Ditto for kitchen stuff (if you don't mind all of the wrapping paper).
The first part is the computer stuff. Actually, this isn't nearly as bad as it used to be. I can thank Steve Jobs for that, I suppose. The iMac is one big thing that doesn't have to connect to a bunch of other things. Well, in my case it does, but it's just a handful of USB things, and an external monitor (which just doesn't look as good as, say, one of those new matching 27" monitors they make now :)). In the old days, I'd have a bunch of different stuff to connect into it, and there would be this big separate tower and what not, with six different kinds of connections to it.
The TV and audio stuff, however, is still a huge pain. It's also not as bad, since you now replace your VCR, tape deck, CD player, DVD player and what not with fewer devices. While those thing have been consolidated with fewer boxes, there are newer boxes now, namely video game consoles. The funny thing is that I only really use the Xbox. The Wii has been turned on maybe once in the last year. But all of this crap eventually has to route through the stereo as well, and it has wires for five speakers. I can't believe there isn't a better way, today. Granted, HDMI is a step in that direction, but not many of my things have HDMI, not the least of which is my 2006 TV.
There is a little bit of angst with the knowledge that I'll have to do this again in two years or so (sooner if I could generate 60-80k in cash for a house, and the old one went away). And who knows, maybe someone will figure out how to make more of those wires go away.