I'm one of the carry-on only people. I have a rubber travel clothesline and a sink stopper I bring with me, neither of which takes up any room at all. I usually bring one Woolite packet for each day of my trip. I'm very good about soaking whatever I wore that day in some Woolite at the end of the day and then hanging it to dry overnight so I never run out of clean clothes. I also use the hotel drycleaning when needed. However, some hotels have washing machines, which is really nice... I usually try to find this out in advance if its a long trip. Detergent, though, can be iffy.... you never know what will be available... it could be very harsh or it could be nice and they're charging some unreasonable amount for it. I found these Purex detergent/dryer sheets in Walgreens before my last trip, though, and picked them up, thinking they could be good.. they're solid, not liquid, and not even messy powder or anything! They fit nicely without folding into a quart size ziplock bag, too. We brought them along for a trip to Europe after doing a test run on a load at home and they work beautifully. These are great for travel if you plan to wash clothes in a washing machine while you're away.
http://www.purex.com/purex-3-in-1
Just thought I'd share.
P.S. I also like to carry a 3 ounce bottle of Febreeze along. If I'm sink washing, its nice to have a backup if you don't think things are washing out freshly enough for you. Just sink wash and sniff... if you're not pleased, spray with Febreeze, let dry, sink wash again... and perfect.