Google keeps ping alive on their 8.8.8.8 nameserver, but that's probably just being polite. Most providers would rather block off ICMP than have to deal with the risk of getting flooded now and then.
Out of curiosity, how would you mitigate a similar DDOS attack against your system? Do you believe that your system would hold up against a DDOS similar to what NameCheap is experiencing?
While I agree with not locking yourself into one company for a lot of services, I'm not sure that using a third party DNS server puts you in a better position. The Namecheap servers were knocked offline by a DDoS attack. Do you believe that third party DNS servers are more resilient to that type of attack? At least with a registrar provided DNS server, you're a paying customer and so you can probably expect some form of customer service that you might not get with a free offering.
CloudFlare is probably better set up to deal with that kind of attack because they have a paying customer base and specialise in resilient website operation, but whoever you're with, if a DDoS is big enough it'll be hard to protect against.
If you are evaluating 3rd party DNS, I developed a tool for testing recursive dns query latency here http://cloudharmony.com/dnstest - the test covers most major Anycast providers.
We have also created a report that summarizes and aggregates manged DNS performance and availability globally and regionally, features and pricing. It is still under development, and we intend to sell it in the future, but I'm happy to share it, and would appreciate feedback (caution it is a 10mb file): http://dl.dropbox.com/u/20765204/CH-DNS_Report-12_2011.pdf - it is a good resource if you are evaluating different providers.
<b>Fatal error</b>: Call to a member function getAffiliateOrStandardUrl() on a non-object in <b>/var/dropbox/deploy/cloudharmony/lib/util/CH_SpeedtestUtil.php</b> on line <b>802</b><br />
Still waiting. Unfortunately, I can't seem to transfer the DNS from namecheap to Dynect, my usual DNS provider. It keeps on coming back as "Please try again. 541."
Also, it's been on my todo list for at least a month. No excuses on my end.
This is odd, I managed to move my DNS hosting away from NameCheap about an hour ago and my domains are back up... Make sure you click "My domains - Domains - Transfer nameservers to webhosting"