Depends on your needs, but it is fairly simple to buy a domain-name and manage the dns-servers and hosting of web-server (and I guess e-mail) yourself.
If you have a A/AAAA-record in your top TLD pointing directly to your nameservers you do not depend on anyone but the root servers and TLD-servers to be available (in regards to DNS). Now, you just need to find a TLD that is not managed by one of the big ones, but that should be fairly easy.