Your question is interesting and actually has two answers. According to a link from Oxford Dictionaries (which I've included below), more words in the English language contain the letter "E" than any other. This was true in the 1800s and it is still true today. However, your question asks which letter has the most entries in the dictionary, and the answer is "S."
The reason for this seems to be the vast number of blends (st-, sc-, sch-, sh-, sk-, sl-, sm-, sn-, sp-, sw-) formed from this letter. The letter whicih comes in second on the list is "A."