I think this is field-specific and very much depends on what is valued most: the statement of the result or the proof.  This especially goes for solutions of well known open problems, so as to avoid <a href="http://mathoverflow.net/questions/26821/is-thompsons-group-f-amenable">these kind of stories</a>. 

For example, in *Enumerative Combinatorics* and *Discrete Probability*, two areas close to me, these priorities are sort of opposite.  In the former, there are very few open problems.  A nice new formula or a new bijection construction, even if only conjectured and checked by a computer, is already a lot of progress.  Once you convince yourself that you can finish the proof, you can start giving talks - people will trust your judgement.  

However, in Discrete Probability, there are lots of open problems and conjectures, often delicate and technically difficult.  I would advise NOT to speak about your results until the proofs are fully written and carefully checked by somebody.  This might work once or twice, but eventually there will be a seemingly trivial mistake which you overlooked in the first draft.  Unfortunately, often enough such mistakes can completely destroy your proof.