Sometimes you see other people earn a badge which makes you curious to whether or not you have that same badge, you could go to the encyclopedia, but it would be convenient for us if implemented.
+1. I thought of this as well a while back--it would be very nice to be able to see what badges you have in common with someone.
I'm not sure I understand Rook's specific suggestion here, so maybe I'm just restating the same idea--if so, sorry! I think it would be good if the encyclopedia page for a single achievement/badge indicated whether you had that badge. The information is available now on the full list Achievements page but you have to look through the list to see if the specific achievement is checked and greyed.
This approach would avoid making it into a "compare every badge with other Glitchen" feature, but allow for a "their feed says they just earned this and I'm curious if I have it too" thing.
Don Monkey, there is a "Hide achieved" link/button on the Encyclopedia's Achievements page that will automatically hide ones you already have and show which achievements you still need.
An unofficial achievement comparison tool can be found here: http://glitchium.com/badges/compare/
Unfortunately the API does not have any methods for listing player achievements, so the data will have to be manually scanned (and thus may not be up-to-date until you scan the achievements for the players you wish to compare).