because of the relationship eNom has with a self appointed health/drug czar, whose name I just cannot recall at the moment.
LegitScript, I think.
Marcia, why are you wanting to move out of Godaddy? Perhaps some specific reasoning could helps us recommend a better registrar for you.
Personally I don't trust godaddy, but they're great for $1 and $3 domains. Normally my $1 domains get moved out of there 61 days after registration because I simply don't trust them, but I do have a few I've left sitting at Godaddy that are totally unused and awaiting development or resale.
I would have recommended Name.com but like Stub said they were bought out by Enom. I won't be moving domains out unless something happens, but I'm anxious to see how everything shakes out before I continue moving names to Name.com. Based on past experience, and the new promise to let Name.com continue operating as they have been, they should still be a safe option and a good choice.
Dynadot is a great option, as mentioned.
NameSilo is a new one with low prices and free privacy that I'm starting to like more and more. I have a few low priority domains there without any problems whatsoever.
Internet.bs used to be one I recommended a ton. But first they had paypal, then they lost paypal, and now there's a whole slew of payment options to use. My bank always seems to give me some kind of "International Processing Fee" for buying there, and Ive used a few different cards. It amounts to roughly 35 cents for every 20 bucks spent. If you don't get that fee they're great, and I still keep domains there even with the fee, but I think I'll start using NameSilo instead.
Moniker is another one I used to recommend many years ago, but they've been bought and sold a few times and have gone downhill with both support and also technical errors like not being able to unlock domains, trouble renewing domains, Moniker having problems contacting the registry, and screwups with their whois privacy. I have almost all of my domains out of moniker and don't recommend them any longer.
Namecheap is decent enough, they used to be pretty cheap. They're not that cheap anymore, plus they're an Enom reseller and don't have their own backend yet (which has been under development for quite some time I believe) and there are other better options. I'm slowly moving all my namecheap domains out of there now.
Fabulous is where I keep all my high value domains that I want to keep for a long time. Great security options. I have an account with $8.99 .com pricing which is great, but the regular retail pricing is $29.95 which isn't so great if you don't qualify for a cheaper account.