There’s an innumerable amount of Overdrive pedals these days – but this can’t hide the fact that many of them are based off a limited number of “reference” pedals. This is (most likely incomplete) list of such reference pedals, in no particular order.
Quite likely the most famous overdrive pedal. It is known for soft clipping, a pronounced bass cut and a mid-boost. Ibanez themselves have produced a large number of varieties, and practically every pedal manufacturer offers some Tubescreamer variation. The Boss SD-1 is very similar.
The Proco Rat is one of the best-known distortion pedals. The Boss DS-1 is a similar design.
The Fulltone OCD is often considered the benchmark for an amp-like distortion pedal.
Much of the Klon myth is to due its limited availability and hence insane prices on the second-hand market. It is a transparent boost/overdrive with a slight mid boost, often used as “always-on” pedal. Many copies are available these days.
Bluesbreaker & Guv’nor
The Marshall Bluesbreaker is one of the original “amp in a box” pedals, trying to replicate the sound of a Marshall JTM45. Other Marshall in a box pedals, such as the Marshall Guv’Nor aim at recreating the sound of a Plexi or JCM800, and often include a full Treble/Mid/Bass tone stack
The Boss Blues Driver is a popular “full-range” overdrive, without the pronounced mid boost of the Tubescreamer/SD-1.
The Hermida/Lovepedal Zendrive is renowned for “Dumble-like” overdrive, meaning that is produces the smooth overdrive for which Dumble amplifiers are famous.
The Cochrane Timmy is a pedal to which the overused term “Boutique” still applies. It is a transparent overdrive, meaning that it doesn’t color the sound very much.
The first overdrive pedals were fuzz pedals, with the Fuzzface (these days made by Dunlop) famously being used by Jimi Hendrix. It is still sold in its original round form, including mini variants.
Another famous distortion/fuzz pedal is the Electro Harmonix Big Muff. Many variations have been built throughout the years.