This answer is mostly a synthesis of the useful discussion found above.
I don't think English is unusually well-suited to Limericks, or, more broadly, highly structured rhymes. One poster mentioned a Russian analog, and in Spanish there is the Quintilla.
I would say that there are a couple of preconditions that a language must meet:
A low average syllable count, so that syllable count problems can be solved more easily. I don't speak German fluently, so I can't say for sure, but I think this criterion would rule it out.
A high proportion of words with terminal vowel sounds for rhyming. Again, I don't speak Hebrew, so I can't say for sure, but I think this criterion would rule it out. As a poster noted above, Italian is probably the best language for this one.
I think the poster above is on to something with the note about dactyls...without a smooth dactyl, you can construct these patterns, yes, but they'll be quite choppy. I have trouble imagining a language without dactyls (though I could imagine a pidgin, I suppose).
I will hazard a guess, here, so take cum grano salis: if English is especially conducive to these criteria, I would say that it's because it is because it is so derivative of other languages. Whatever deficiencies one source may have are pasted over by words rooted in other languages. The example below relies almost entirely on Greek roots for the dactyls, and Germanic roots for low syllable count:
The limerick packs laughs anatomical
In space that is quite economical,
But the good ones I've seen
So seldom are clean,
And the clean ones so seldom are comical.