Here at HillCountry Dachshunds we do the following health testing on all of our adults:

PRA (cord 1) testing
A genetic DNA swab (can be done at any age so we do it as soon as possible.  Done only once.

Patellar luxation
A physical exam of the knee done by a vet (done at one year of age or later).  Done annually.

CERF testing
A physical exam of the eyes done by a licensed ophthamologist - done around a year and then annually (or bi-annual if there's a potential problem we're monitoring)