Sooner or later, anybody who corresponds with me for any length of time encounters my use of “hahae” as an inter- jection of amusement or laughter. A quick search reveals that it’s even popped up here in my blog. My friend, N.E. Brigand, actually asked me about it late last week, so it seemed an explanation might be in order.
There are perhaps two surprises here. 1) I’ve been using it — in various reduplicative forms: e.g., hae, hahae, hahahae — for something like twenty years now. And 2) I didn’t make it up.
It’s actually an attested Latin interjection of laughter. It’s even in my Harper Collins Latin Concise Dictionary (London: Harper Collins, 1997, p. 97), and it’s certainly in some of the bigger Latin and etymological dictionaries. 
As it happens, I crammed about three years of Latin into a single year of high school back in 1985-6. I’d started teaching it to myself — a bit here, a bit there — during junior high school, and especially during the summer before I started my freshman year of high school — in fact, I’d done the same thing with French before I took it in junior high school (and later, all through high school as well). In both cases, it gave me a substantial advantage over my classmates, and in the case of Latin, the teacher put me right into independent study after the first two weeks, whereupon I worked my way through three years of high school Latin, just me and my trusty Wheelock — and only a periodic assignment or test from the teacher. Like I said, independent study! (And by the way, the same thing happened again at the end of high school, when I’d exhausted the official curriculum for French. You’d think I’d be more fluent, wouldn’t you? :)
At some point, I encountered hahae reading Roman drama. It’s particularly conspicuous in the works of Terence and Plautus. (How I wish I could have said Terrance and Phillip here, hahae. You see? There it is again! :) There’s actually a whole section on Terence’s use of hahae in a published thesis with the accurate but not very thrilling title, The Interjections in Terence, which I happened upon very recently. 
I began using it immediately myself, most often (in those days) written with a pretentious, unnecessary diaeresis, like this: hahaë. I got my friend, Gary, doing it, too, and we’re both still using it to this day. And what about Pugnax in the title of this post? Well, these plays I was reading always seemed to have a hot-headed protagonist called Pugnax, so in the early days of the adoption of hahae, we seemed always to be adding “quoth the mighty Pugnax”, or something similar, in parenthesis. Yes, we were actually saying this at age fourteen or fifteen. I know, I know — we’re as amazed as you are that we weren’t more popular with the ladies. They really missed out! ;)
 Speaking of etymology, there are closely related forms and cognates attested in a variety of other languages. Most of these are probably onomatopoeic in origin, which must account for the preponderance of similar forms across language families. A sampling: French haha; Old English, Middle High German, Old Frisian (ha)há; Middle English ha3e, hahe “pleasure”; Middle High German hage “pleasure”; Hungarian hahota “loud laughter”; Finnish hahottaa, hohottaa; Arabic kahkahah; Greek κακάζω, καγκάζω. And do you really want the sources?! I’ll add them if anybody does, but I’m not so sure people are really interested that after all. Suffice to say, they’re mostly the usual suspects (e.g., Skeat, Stratmann, et al.)
 Newton, Walter Russell. The Interjections in Terence. Thesis for Syracuse University. Portland: Andover Press: 1899, pp. 33-34. Newton explains that “[t]his interjection is not used in Terence to express hearty, sincere amusement, but is usually ironical, derisive, or contemptuous.” Who knew? :)