Counting the Endpoints of an ASCII Art
Snails, 29
A
\+|\-)lr!\-|(\+|\|)n!\|}!\+

I added line comments with ,,, in order to make a commented version.
A                    ,, Count all accepting paths
        \+ | \- )    ,, Literal '+' or '-'        
        lr           ,, Set direction to left or right
        !\-          ,, Assert next char is not '-'
    |                ,, Or...
        ( \+ | \| )  ,, Literal '+' or '|'
        n            ,, Turn 90 degrees right or left (from initial direction right)
        !\|          ,, Assert next char is not '|'
}                    ,, Group everything previous
!\+                  ,, Assert next char is not '+'