I built up good rankings with search engines over the years with my old domain. I recently changed my domain name and have all the links 301 redirected from my old domain to my new domain. I also used Google's 'change of address' tool to help index my new domain faster. Will this affect my rankings at all?
Assuming no other changes aside from the domain name were made, your Ranking shouldn't change.
301 redirects essentially say "The content you are looking for has moved to a new Address, here it is. Oh, from now on, you don't Need to come back here anymore looking for Mr. Content, he has moved permanently."
PageRank is also "redirected" via 301 from The old Domain to The new One.
If your new Domain name happens to contain relevant keywords, though, your Ranking might improve over Time.