Bases are the opposite of acids and so can also be defined in many ways. Again the two most common definitions are Brønsted-Lowry acids and Lewis acids.
A Brønsted-Lowry base is defined as a species having a tendency to accept a proton. (page 181, Organic Chemistry, Clayden et al, Oxford University Press 2001)
A Lewis acid is defined as an electron donor. (page 152, Inorganic Chemistry, Housecroft and Sharpe, Pearson Education 2001)
For the discussions here the Brønsted-Lowry base is more appropiate as the Lewis definition is primarily concerned with inorganic molecules
Below are five examples of common bases

All of these molecules, when in water, will form hydroxide ions (OH–).
On to pKb