Units get a defensive bonus when you put them in "Fortify" or "Alert". But sometimes I just want to pass them over for a single turn. If I select "Do nothing" (or hit space, which is the same thing) do they still receive the defensive bonus?
No they don't, this unit simply didn't take a turn - with the exception that the unit is stationed on a tile that provides a defensive bonus (for example a fortress) or they're on rough terrain.
A full list of conditions and bonuses as well as base statistics for each unit type is detailed in this article. Of particular note is the following;