Vinyl baseboard is an inexpensive material that can withstand a lot of abuse. It's most commonly seen in retail stores and other public locations, but it's becoming more popular in homes. Vinyl baseboard is available in many colors and textures, so all you have to do is cut it and glue it in place. Using the right glue will help keep the baseboard in place for many years.
Acrylic Base Adhesive
An acrylic-cove-base adhesive is most commonly used in commercial applications. If you want to use this in your home, you certainly can. This type of adhesive is designed to provide an instant adhesion, is easy to apply and easy to clean up. Since it does grab the material almost immediately, you need to take your time when you place the baseboard, since you won't have much time to reposition it should you need to.
Solvent Free Glue
This is a more 'green' way to adhere vinyl baseboard. You can find several brands of solvent-free glue. These take a little longer to dry, but will still give you a solid adhesion. Since there are no solvents used in the formula, there will be little to no odor when applying it or after it has dried.