$\pi$-Base, which draws its data from Steen and Seebach's Counterexamples in Topology, lists the following separable, non-Hausdorff spaces. You can learn more about these spaces by viewing the search result.
Compact Complement Topology
Countable Excluded Point Topology
Countable Particular Point Topology
Deleted Integer Topology
Divisor Topology
Double Pointed Reals
Finite Complement Topology on a Countable Space
Finite Complement Topology on an Uncountable Space
Finite Excluded Point Topology
Finite Particular Point Topology
Hjalmar Ekdal Topology
Indiscrete Topology
Interlocking Interval Topology
Maximal Compact Topology
Nested Interval Topology
Odd-Even Topology
One Point Compactification fo the Rationals
Overlapping Interval Topology
Prime Ideal Topology
Right Order Topology on the Reals
Sierpinski Space
Telophase Topology
The Integer Broom
Uncountable Particular Point Topology