What is a ring modulator?
A ring modulator takes the signal from your instrument, splits it in two and then makes one of them oscilliate into a sine wave. These two signals are then mixed together in the modulator which outputs the sum and the difference of the frequencies present in each waveform. It's a pretty advanced modulation that has been named not because of the ringing sound that it sometimes produces, but because of the analog circuit of diodes inside the original unit used to take the the shape of a ring.
Any good examples?
The ring modulator is a pretty whacked out effect that is more often used in ambient soundtracks, or even in the 20th century classical music (Karlheinz Stockhausen, groundbreaking composer in electronic and serial music, is a famous user of the ring modulator), than in typical guitar music like rock, blues or jazz. Still, there's a few examples and quite naturally many of them involves alternative and experimental bands. An example that might be hard to recognize, due to the small amount of effect added, can be heard on the Black Sabbath classic song "Paranoid" where Tony Iommi adds it to his guitar solo. A more audible example can be heard on several Flaming Lips tracks, something that easily can be noted on the song"Christmas At The Zoo". The ring modulator effect can also be heard all over The Mars Volta debut album "De-loused In The Comatarium", one track where Omar Rodriguez-Lopez emplyos the effect a lot is "Roulette Dares (The Haunt Of)". Trent Reznor of Nine Inch Nails is famous for using weird effects, the ring modulator being no exception as it can be heard on songs like "The Becoming". Devo uses it on their cover of "(I Can't Get No) Satisfaction" and Japan takes it for a spin on their song "Ghosts". A more modern user is Josh Homme who has modulated his tone with a ring modulator on the Them Crooked Vultures track "New Fang".
Which pedal should I get?
If you´re into crazy effects and need a ring modulator there's some good options out there. The Moog Moogerfooger MF-102 Ring Modulator is a classic analog choice while the Z Vex Ringtone is an extremely complex pedal which can create loads of weird sounds. Both the Way Huge Ringworm and the Dwarfcraft Hax has pretty simple controls which always is appreciated. And then there´s the Electro-Harmonix Ring Thing, which apart from the ring modulator effect also includes features such as pitch shifting. Try them out before you buy, or at least check out some clips of them before you know which pedal that would suit your crazy ideas.