Well, the web of trust allows someone to map out relationships between people. That's a privacy issue and may tell people things about you that you weren't ready to share.
One example: Say you're a gay man living in Saudi Arabia. You obviously want to hide that you're gay, so you use PGP to encrypt mails to your romantic partners.
You all sign each others keys, building a web of trust, but you don't think to use anonymous e mail addresses.
Now one of you makes a mistake and is picked up by the police. He manages to throw his laptop into the next river, and he's not easily intimidated, and he used gmail over ssl, so nobody knows who he communicated with. BUT the police finds his key on a public keyserver, looks at the signatures, follows the web of trust/writes down the e-mail addresses, and pays all of you a visit.
That's probably a bit far-fetched, but if I were a forensic analyst, I'd probably look for public keys just as a matter of course, as one stop on my checklist (owning a public key would imply that there was encrypted communication, and I'd probably want to know who with, so signatures would be interesting. Now in my country digital forensic analysts are my friends, but in Saudi Arabia I imagine they might turn out to be a very dangerous enemy).
Another scenario might be that you actually DID use an e-mail address that couldn't be traced back to you, and didn't leave any obvious information in your public key, but then told your family to use that key to communicate safely with you. Unknown to you, two or three family members signed your key with theirs. Wham, you're no longer anonymous. Now your identity can be found by following the signatures of your family members.