General rule of thumb: Take twice the money, and half the clothes that you think you need. I just got back from my second liveaboard, and basically rotated between 3 swimsuits, one or two t-shirts, and a comfy pair of shorts. I wore shoes when I boarded the boat, and not again until disembarking.
As others mentioned, multiple swimsuits are nice so you can rotate between them between dives. Rooms can be chilly due to running A/C to keep the moisture at bay. Long sleeve t-shirts are nice here, plus they offer some more sun protection when outside.I tended to sleep in a long sleeve T as well due to the room temperature, and blankets being a bit skimpy. On this last trip I was also doing the shared room thing, so gotta cover up... :mooner: Also, in my case shared room meant shared bathroom, so having stuff that was easy to change into was nice - stretchy shorts are easier to put on when you're in a small closet like space that's also moving in 3 directions at once.
If you have electronics, take necessary plug adaptors (most boats will tell you what electrical standards they have on board). Many devices now are multi-voltage so you probably just need a plug adaptor, not a voltage transformer. I also found it very handy to have a small extension cord - I actually cut down a longer one and put a new plug on it, leaving the original 3-outlet end on - I could use one plug adaptor and feed multiple chargers, plus it let me put things further from the outlet in situations were plugs were not that convenient. If you're tying to conserve weight/space, see what things you can re-use too - I used my iPad charger to charge the iPad, my camera (GoPro), cell phone, and power an external hard drive. If I do this again, I'd probably take a second iPad charger brick.
Consider some personal business cards - makes it easy to give your info to anyone you might want to keep in touch with, or to exchange photos/videos with. Also consider bringing a decent sized USB thumb-drive, or even external HDD in case you want to exchange pictures with other people. If you don't bring a laptop, frequently the boat will have a computer for public use. Just make sure that you have good anti-virus on whatever you plug your stuff into next - they don't always get updated that often!
Some fix-it stuff is nice to have handy - a few zip ties, some duct tape, etc. Probably not a full save-a-dive kit though - if it's common stuff, you can probably rent it if it breaks.
Even if you're in "warm" water, doing multiple dives over multiple days will suck the warmth out of you, so plan accordingly - the 3mm suit might be fine for the first few dives, but by the end of the week you might be wishing you had something warmer.