I realize a similar question has been asked before but what I want to know is a little different and is not answered by the link in the answer to that question. I am interested in knowing the best known general upper and lower bounds (non-asymptotic) for an arbitrary Ramsey number $R(k,l)$. Similarly the best known general upper and lower bounds for an arbitrary diagonal Ramsey number $R(k,k)$. It would be good if someone could also tell me asymptotic bounds in these cases as well.(I am not sure whether wikipedia is upto date.)
I suggest you take a look at this paper by Radziszowski. This site is also up to date with new results about $R(k,l)$.