I use Rabbit Register by Evans Software
Evans Software Services - Rabbit Software
I have used this since 2010 and I absolutely love it. It's really a thorough program which includes pretty much everything other programs have, plus some unique features. Mr. Evans keeps everything up-to-date with ARBA changes, including new breeds, new varieties, licensed ARBA judges, etc. It builds exportable pedigrees that work to share with other RR users, as well as .pdf versions that everyone else can read. You can read about all the features at the link above.
It's not free, but you buy it once; no annual fee, and lifetime updates are free (and they really are - I haven't paid a dime since my initial purchase). The program and your data are on your computer, so nobody else can access them (especially because I keep my rabbit-related finances there, that's important to me), the program and your data are accessible even if the web is down, and your data won't evaporate like it can on a web-based program, if the host quits.
The tech support is phenomenal. I am not a techie (that is putting it
very mildly) and Mr. Evans has been super responsive over the years with my stupid questions, as well as my suggestions and requests.
The Deluxe Version costs $20 more than the Standard Version, but it's been so worth it to me. The Deluxe includes a genetics program which not only fills in the genotype of any given variety, but lets you do virtual "test-breeding" to predict what colors might come of any particular pairing. It is also responsive to data entered about animals' offspring, adding information about genotypes retroactively (e.g. if a black doe produces REWs, it adds the recessive
c to the doe's genotype).
Best of all, you can get a 30 day trial run for free. The demo is the Deluxe Edition. All data you enter into the demo version (which is on your computer) will transfer directly into the purchased version if/when you buy it, and for me the transition was seamless. If you choose the Standard Edition, all of your data will still be there, you'll just lose the Deluxe Edition features.
So there's my two cents.