I was wondering if it is possible for me to run my own DNS server even though I have a dynamic IP. I heard if you keep the TTL's low, it shouldn't be a problem. Would this actually work and be useful, could be done, but not practical, or simply no chance in hell?

Do you mean that your server you wanna run the DNS on has a dynamic IP?
Well, you can surely do that but what for?
DNS clients have the DNS server's IP address hard-coded in their IP config. Or if they use DHCP, it is hard coded in the DHCP server. So if your DNS server has a dynamic IP, well, when its IP will change, clients won't be able to resolve no more as they'll keep trying to connect to your old DNS server's IP, unless you manually change the IP config of all the client or of the DHCP server...
Now if this is about learning stuff about DNS, why not?

it could be acheived by building a script that would check it eth0 Ip's have change. If so, it would change the "router" entry in your host.conf file then do a route del default , route add default gw router eth0. Then restart dhcpd. named should not notice it as the dns servers have not changed, just your IP. But just in case, restart it too it only takes a few secs. I'm not sure enough about this to let you restart only the dhcp server. Personally I would restart every server that do something out of my external IP (I'm paranoid).

happy new year

If you want to make a DNS server for just computers sitting on your local network, that works great no matter what your Internet IP Address does.

If you want to make a DNS server so computers out on The Internet can use you as their DNS server or as the nameserver for a domain you own that isn't really a good idea with a dynamic IP. The fact that your IP could change means there will be some time between when it changes and your TTL where systems on The Internet can not see you. Using a lower TTL will just put more load on the computer listing your DNS entry and that computer is usually not under your control so you can't likely change it's value anyhow.

The idea of DNS is that there will be known good IP addresses that have servers to resolve names, this whole concept is violated when you try to put one of these servers on an IP address that could change. If it's just for your local network, that is fine because then the system will have it's dynamic Internet IP and an IP address on your internal network that likely does not change.