Scale length

Measure from the nut to the saddle- in other words, the portion of string that vibrates when plucked, w/o fretting. Most basses are 34" but there are many variations. 30, 32, 35, 36...

 

Since bridge saddles are often not a consistent distance from the nut, you can also measure from the nut to the 12th fret, and double the length.

 

Scale length does NOT determine the "scale strings" you need.

Strings should really be sold by overall winding length rather than "scale length".

This article will explain how to find the correct length strings for your instrument:

Finding the correct string length for your bass.

 

What Jason said. And also 33 1/4 is used by Rickenbacker.

 

Yes... Jason is wise! You need to consider the WIND length needed to clear the nut and the tuning posts (nothing to do with silked or non-silked strings), or you run the risk of weakening the core and breaking the string. I just went through this with a set of "standard long-scale" strings for a 34" scale bass which ended up with the low E winding 1-1/2 times around the post - this is a BAD thing. On Jason's recommendation, GHS's "standard" scale length solved the problem.