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I'm looking for an index of common rhythms. This video shows basically what I had in mind, only it is for the bass.
I'm pretty sure there has to be names and a list somewhere for the common rhythms of kick, snare, kick, snare, or kick, snare, kick kick snare etc.
This site here has quite a few examples of rhythms, whether they be from well-known songs or just something to groove along to. http://www.onlinedrummer.com/beats.php
I know I have something that was from Vic Firth which outlined about 40 or so basic rhythms from rock to jazz to latin:
Suggested by Rene Marcelo: Try: Drumset Playalong Tracks
The one I was thinking of showed more basic grooves, but that link fits the bill nicely I think.
As Zajn mentioned, Vic Firth does have an extensive education resource section. The 40 essential snare drum rudiments are probably less applicable here, but you can find 12 "Essential Grooves" plus six more in part 2. They are part of a video series with Vic Firth Artist Tommy Igoe, but the drumset notation for each basic groove is provided on the site for free.
For the sake of being comprehensive, I would like to introduce you to the 40 Snare Drum Rudiments (Wikipedia link) alluded to in previous answers by others on this page.
They are a set of exercises for snare drum alone, to learn basic patterns that are applicable in all types of Western music, and which are useful to develop rhythmic accuracy and dexterity.
The Rudiments started to be codified in the year 1612, for use by military snare drummers on the battlefield, according to the Wikipedia article referenced above. To this very day, all drummers of any and all styles of Western music who get formal training start by mastering all of these 40 rudiments on the snare drum before they go any further in learning to play drums. [I remember reading an interview with the famous hard rock drummer Tommy Aldridge who said that even though he is entirely self-taught, he started out playing drums by teaching himself the 40 rudiments on snare from a method book, and did not start adding additional drums to his kit until he had mastered playing these rudiments on solo snare.]
