As hinted by a not entirely moronic Hungarian, it strongly depends on which "types" you allow.

http://primepuzzles.net/puzzles/puzz_225.htm has some possibilities.

It's easy to construct rare prime forms by picking a quickly growing function with one or a few early primes. You mention Generalized Fermat 10^2^n+1, but there is no base b with

*more* than 7 known primes b^2^n+1, and finding one with more than 10 looks very hard. The record is 7 for b=2072005925466 at

http://primepuzzles.net/puzzles/puzz_399.htm
If you want relatively notable named forms then some candidates are at

http://en.wikipedia.org/wiki/List_of_prime_numbers (look for comments like "only known").

In addition to your list of proven repunit primes, there are known probable primes for n = 49081, 86453, 109297, 270343.

There is no known Wall-Sun-Sun prime although infinitely many are expected to exist.