Google Suggest is pretty neat. I'm used to local browser auto-complete, where my previous entries into similar input-fields are offered as completions of my partial typing.
Google Suggest does the same based on their server-side, 'global' view of potential completions. Up to 10 potential completions are shown, apparently in order of how often they're searched for by Google users.
The updating of the list with each keystroke is instantaneous, with no noticable network lag -- so there must be some smart preloading (of compressed tables?) going on behind the scenes. (I haven't had a chance to peer behind the curtains and watch the javscript/http yet.)
They've blocked out common porn-related terms, but common misspellings are still there. Topics which some nations censor ('taiwan independence', 'mein kampf', etc.) are still present.
If suggestions are in fact ranked in order of search frequency, Google Suggest is leaking some very interesting information to outside interested parties -- the equivalent of Google Zeitgeist, but to a much greater depth (sliced by query prefixes). But it's probably the case that any major competitors already have their own strong windows into popular queries anyway, so they don't feel the need to guard this info as proprietary.
Anyhoo, Rachna and I came up with a couple of games you can play with Google Suggest:
Google Boggle: Decide on some search prefix, such as 'tre'. Each player writes up to 10 guesses of what the suggestions for that prefix will be. Winner is who guesses the most that round. Repeat as desired.
Power of Suggestion: Pick some search phrase -- a name, an event, a quote, whatever. One player guesses how many characters have to entered before that phrase appears in the suggestions. The other player can choose 'over' or 'under' that guess. Whoever's closer wins the round, and choosing order alternates.