Turkish is commonly cited as an example of a language which is, with only one or two quirky exceptions, exclusively suffixing. Cross-linguistically, suffixing is much commoner than prefixing and I have heard that no language is as prefixing to the same degree that Turkish is suffixing. I am aware that there are various languages (e.g. Russian, Swahili, Navajo, Nahuatl, Kuot) that do make relatively extensive use of prefixes but does anyone have any idea which languages are the most prefix-heavy? (is it perhaps one of the aforementioned?)
Athabaskan languages would be the "most prefixing", in (a) being almost or in fact exclusively prefixing and (b) allowing many prefixes (11 positions). Papers on Navaho include this, as well as J. Kari Navajo Verb Prefix Phonology and Young & Morgan The Navajo Language. One can check information from the related language Sekani, and it seems that the language Slavey (K. Rice, A Grammar of Slave) has over a dozen prefix positions. Another contender is related Tlingit, which however has more suffixes.
I would vote for Swahili (the fact that it's the only language there that I am intimately familiar with notwithstanding), I can confidently say that almost every word can be conjugated by adding as many different prefixes and suffixes as necessary to convey a particular meaning. Especially when it comes to verbs, the prefixes can be especially many since they convey gender (of both the subject and the object), whether they're being referred to in the 1st, 2nd or 3rd person, the tense in which the action is happening, the relation in terms of distance between the subject and object (near or far) or whether the action is being negated. Each of this things is usually represented by a different morpheme in the form of a prefix.