I'm looking for stuff that specializes in something that isn't super common, or is just a standard Synth or other sound design utility (sampler, effect, etc), with a not-so-standard function that can be really useful.

An example that I've seen mentioned on the forum is PaulStretch, which can stretch a sound up to like 10,000x or some crazy number like that, while still making the sound useable by using spectral smoothing or something weird like that. There are tons of plugins that can stretch sound, but with extreme stretches the sound generally loses its integrity, and I've yet to see another that stretches it for as much as paulstretch.

Things like that.

There was this Autogun plugin by IL few years back essentially having one of their synth engines under the hood, but with only a one selector button on the top.

Even more interesting plugin appeared at one of the KVR developer challenges that made the presets totally random. That was kind of cool. Can't remember name of it...
EDIT: Oh here we go: http://www.kvraudio.com/product/the-element-of-surprise-by-ugo

Native Instruments Flesh looks like a pretty intriguing sound design/composition tool.  It's a Reaktor ensemble/instrument made by Tim Exile.  It seems like its geared toward groove resynthesis, rather than patch creation, but I've never actually used it, so I'm not sure exactly what its limitations are.

http://www.native-instruments.com/en/products/komplete/synths/flesh/

grm tools, soundhack, etc

+1 on soundhack stuff

here is some other pretty quirky stuff I like:

http://aegeanmusic.com/doppler-dome-Specs (Simulates the doppler effect)
https://soniccharge.com/bitspeek (It's like a vocoder that makes you sound like a speak 'n spell)
http://www.tokyodawn.net/proximity/ (simulates distance of an sound w/ various means)
http://www.loomer.co.uk/shift.htm (a pitch shifting plugin based around grains)
https://www.native-instruments.com/en/products/komplete/effects/the-mouth/ (Turns any audio input into melodic output)