Why are amidines more basic than amines?
Note that when you are comparing amidines with amines, you are comparing 2 nitrogen atoms with 1 unless you are comparing it with diamines.  Amidines which have 2 ionizable nitrogen atoms are stabilized  by 2 resonant structures, therefore making them more likely to accept protons (that is more basic).  Similarly, guanidine (not to be confused with guanine which is a nucleic base) which has 3 ionizable nitrogen atoms are stabilized by 3 resonant structures thereby making it even more basic. 
For additional reading, check out the basicity of the following drugs.
Betrixaban (which has 1 amidine group)
Pentamidine (which has 2 amidine groups)
Guanethidine (which has 1 guanidine group)
Metformin (a biguanide, that is, having 2 guanidine groups fused together)
Altretamine (which has 3 guanidine groups fused together into a cyclic structure)
Famotidine (which has 1 amidine group and 1 guanidine group).