Stockpiling rags is always a good option. You can even cut up your old towels and turn them into rags instead of just throwing them away. Dirty rags can become stinky and because they are wet are susceptible to mold, so make sure to rinse them after use and  dry them until you can store up enough dirty rags for a load of laundry. You can also purchase a spare terry-cloth or sponge (maybe two- one for the floor and another for the counter) which last much more than one use and can be bleached if it builds up enough grime. Again, you would have to put in a little extra effort as you would soak it in soap after each use. EcoTowels are a German brand that are essentially reusable paper towels. You can check them out at their website here:

 http://www.bambooya.com/bamboo-eco-towel.html

Obviously overseas shipping is not very eco-friendly, but investing in alternatives to paper towels definitely is!