I've seen a few Twitter visualisation tools, and the HiveMindMap is one of the most attractive. Just take a look:
You can search for particular words or tags, but it's not (meant to be) comprehensive, so you'll only get the recent stuff. You will see links between terms, with the thicker the line, the more important the connection. You can drill down into the words, getting information on a phrase, related terms, key users and so on. It's not just pretty, it's quite useful as well.