There are plenty of other reptiles if you allow fractal reptiles.
There are four examples of such reptiles in [here][1] ([Wayback Machine](http://web.archive.org/web/20151117160714/http://users.math.msu.edu/users/ywang/Reprints/reptile.pdf)).

[One example is the dragon fractal.][2]

For polygons, your examples are the only ones.
For *rational* reptiles, (see reference) there are an additional four 2-reptiles for the plane, which are fractal. It is unknown if there non-rational 2-reptiles, but conjectured that there are none. A reptile is rational, if the rotations needed to get the two parts are all rational multiples of $\pi$ (if I am not mistaken).

  [1]: http://www.math.msu.edu/~ywang/Reprints/reptile.pdf
  [2]: https://en.wikipedia.org/wiki/Dragon_curve