Of all the languages for which there is sufficient data, including extinct languages, which vocalic speech sound, or phone, as represented by the IPA, has been used most?
In spoken language it is very likely the schwa [ə]. The schwa is frequent in speech due to a common form of vowel reduction, centralization. This is especially present in rapid speech where vowels may not be perfectly articulated all the time. Also, many languages that are written abjad-wise have the schwa as their most frequent vowel phoneme.
The answer primarily hinges on the meaning of the construction "has been used by more languages, with more frequency than any other", especially whether "with more frequency than any other" adds anything to the question, i.e. whether it means "and occurs with greater token frequency than any other". Since I cannot think of any reason to interpret the clause in that way, I assume that is just another way of asking which vowel is found in more languages. The top contenders are [i] and [a], which in UPSID are a dead heat (language count i=393, a=392). Schwa on the other hand only appears in 134 languages. I would say that it is currently unknown which of a vs. i is found in more languages.
A or/and E.
Vowels are much more of a continuum than consonants. Within each language different vowels are separated by different contrastivity, like height, backness and roundness. These contrast lines are very much dependent on how many different vowels the language is believed to use phonemically.
One way to describe these vowel sounds, is to write them in plain writing, using the appropriate alphabet. This is not the same as IPA-alphabet, but it is still the most frequent way to describe a vowel sound. It is also a way to actually making continuus vowel sounds to be discrete.
There exists several lists counting letters in languages. This Wikipedia page gives an overview: http://en.m.wikipedia.org/wiki/Letter_frequency
The question is also difficult to answer, because you are mixing frequency of languages and frequency within languages. What counts most, people talking, percentage of usage worldwide, or percentage of usage within each language?