For a project I'm working on I will have multiple servers and lots of subdomains (eg- *.mydomain.example). I'm thinking of getting this SSL cert from godaddy- Unlimited Subdomains (Wildcard) $199.99/yr
Will I be able to use the cert on all the servers or do I need to buy a cert for each server since they each have a unique IP address?
Certificates are bound to a hostname (or wildcard hostname), so you're fine using the same cert on multiple machines.
However, when requesting a certificate, you usually create a private key on one of the servers. This private key needs to be copied to all machines in addition to the actual certificate that you receive.
One scenario is where you have www.domain.example resolving to an IP of a load-balancer, which in turn forwards the traffic to multiple servers. In that case, you only need a certificate for www.domain.example that you copy (with the private key) to all servers in your cluster.