My best time for completing a CT speed run is a little under 7 hours, with all side-quests finished. Probably about 6:50ish. I bet if I really, really tried, I could get it down to 6 hours or so. On New Game + of course.
A few tips for anyone who wants to try:
1) Skip every chest, period.
2) Know exactly what to do to trigger events that drive the game forward. (eg, get Marle at the fair, then talk to the girl sitting on the fountain to open Lucca's telepod)
3) Know where the "lines" are that you have to cross to trigger a battle. You'd be surprised how few fights are forced upon you. You can avoid a lot by doing things like hugging a wall.
4) Save often, but don't go out of your way to get a savepoint.
5) If you get into a battle you can avoid, reload from your last save.
6) Some forced fights you can run away from - do it!
7) For ones you can't run from, kill them as fast as possible. Water 2 and Dark Mist seem to be the fastest casting spells thatll kill everyone (on a New Game + anyway)
As soon as the game starts, set the Battle Speed and Battle Message speed to their fastest.
9) Also, set the Battle Mode to Wait.
10) Don't read any dialogue, blaze through it ASAP. A turbo controller helps here.
11) Know all the maps so you can get to where you wanna go fast.
12) While running, you can 'sidestep' to the left and right without losing any forward speed. Use this to your advantage.