One of my favorite patterns to play on the drumset is the group of 3 notes I choose to call "The Ug-Guh-Duhs! I've also referred to them as "The Gadd Triplets," as they seem to be a pattern that he uses in many of his solos. But he's not the only one you'll hear play these - these can be traced all the way back to Elvin Jones and probably earlier than that.
I prefer to call them Ug-Guh-Duhs, because that's how they sound to me once you've applied them to the toms. You can count them as triplets, but because they also work great in a 16th note context I came up with another way to "count" them. Also, saying "Ug-Guh-Duh" out loud as you play, can really help you get the articulation down.
Some of my favorite uses are at the end of a song when you have a "trash can" ending - when the drummer is supposed to make a ton of noise. And I've also used them when I solo, inspired in part of my memories back in college of hearing Gary Novak use them when he soloed with the Maynard Ferguson band (I'm dating myself here). But a part from that, these make great coordination exercises and can really help build your foot and hand technique.
There are several variations and combinations of these, but today I'll introduce you to three of the ones I use. I prefer to put the kick drum at the end of the pattern, but you can also put it at the beginning or in the middle. The first pattern to become comfortable with is:
1. R L K R L K (repeat) Play your hands first on the snare at a slow tempo to get the combination down. Once you feel comfortable with the pattern, move your hands to the toms and cymbals and see what sound variations you can come up with.
The next step is to do the pattern starting with your Left Hand so that you end up with this combination:
2. L R K L R K (repeat) With this variation, practice it the same as you did the first one, starting slow on the snare and then moving your hands from the snare to the toms and cymbals.
Finally, this combination starts to really get fun when you combine the two sticking patterns above into this:
3. R L K L R K (repeat) This is a really difficult pattern to get used to, but sounds pretty amazing once you get it up to speed. One of the variations on this that I like to use is to put the kick drum in the middle of the 3 note group so that you end up with: R K R L K L R K R L K L
Typically you can think of these in a triplet pattern, but try these in a 16th note pattern and see how it goes. Just remember to keep each note steady and equal in relation (timing) with the other ones.