Since my DNS service provider (namecheap) had lots of problems the last days, I'm looking to move my domains to another provider that also offers redundant service. Do you have any recommendation?
Edit I'm looking for a service to host my domain records, not for DNS resolution
Thank you
www.everydns.net is rock solid and run by the people who created OpenDNS. They offer a slave service for free.
Commercial services
Freebies
So all in all, I know clients who use both those commercial services and they are very happy with them. They are not cheap though.
As for the freebies - everydns is my favorite sort of. I am not using them for really important domains though I donate every so often which gives me a couple more options and the track record has been alright so far. Just note, they had their own share of downtime due to attacks etc.. I am not sure what they have in place now but supposedly it's using OpenDNS' infrastructure now.
In general, I'd aim for a global footprint (or scratch that if it is of no concern). It helps when you need to make changes and need them to propagate fast.
Namecheap should be using ENOM's (since they are a reseller), and I am using those as well and haven't seen any hickups. But who knows what they are up to.
If you want to build your own and don't serve 1000s of zones you could rent a couple VPS servers and install PowerDNS or something similar and create your own redundant network. But that requires a bit of system administration and also maintainance.