Is there a right or wrong answer to this question?
Personally, I believe it is always wise to give yourself a little down time in between relationships. You can call it introspection time or for some, healing time. This is the time to reflect back on what transpired in the relationship, to take an honest look at it and yourself and what part you played in it and its demise. What did you learn from it - about relationships and yourself. Do you find that there qualities in partner that you definitely need or cannot bear with? Did you find that there are qualities in yourself that you need to work on or deepen? Did you become a better, stronger person because of the relationship? Or did the relationship deposit a bag (baggage) that you need to work to empty and discard? It is important to make even the most difficult of situations into learning, growth opportunities. Nothing happens by coincidence, but purpose.
I tend to believe that by the third month you can at least begin to consider "getting back in the game." The point is not to jump too soon less you jump straight into a rebound, which is not ideal. If you were in a very deep and intense relationship or was extremely hurt in the relationship, you will need more time.
If your relationship was not that serious, it may take no time to get back into the swing of things. Regardless of the time (how many months, weeks, years, etc), you should always pay attention to your soul. It could be five months or more since a breakup but if your not ready to move on (still hurting, reticent, etc), then it is not time.
You also do not want to get caught up in waiting to get in the game due to fear. Life is meant to be lived. Love sweetens life - makes it more exciting and enjoyable - and sometimes scary and painful. But that is still part of learning and growing.
Long answer short: Take time to take care of you - and live and love life and the people that are brought into your life experience.