One of the most important, interesting and powerful rhythmic tricks available is groupings of three. I don't mean playing 3/4 or 6/8 or quarter-note triplets. Almost every music style uses three-beat figures played in a four-beat environment. In fact, it's rare to hear a tune that doesn't use this concept in some way.
Here's how it works. While playing in 4/4, play figures that are in 3/4. When you count in 4 and play in 3, you'll find that things work out every three bars -- 3 x 4 is the same as 4 x 3 -- so you can play four bars of 3/4 in place of three bars of 4/4. Add another bar of 3 plus one beat and you're back at the start of a phrase.
A popular approach is to play a 3+3+2 pattern over one bar. I'm sure you'll recognize this figure, and you have no doubt played it hundreds of times. One of oldest drum examples is that war horse "Wipe Out". The first bar is plain 16th notes, but the second bar is phrased as 3+3+2, and it cooks.
Also quite common is to play the 3+3+2 grouping over two bars of 4/4: two bars of 3 plus two more beats to get back to 1. The figure you end up with can be counted (and felt) 123 123 12. The result is a sensation of a second rhythm weaving in and out of the time. Check around and you'll find this figure or its like in a lot of tunes.
To take this to the next level, we can play in 3 for extended periods. This is very common in jazz, where the soloist (or the entire band) will switch to a 3-beat figure. It can be a challenge to find your way out of this, but it’s worth it and it always gets a reaction.
If you want to take a crack at this, start by playing a pattern of 3 beats in 3/4 time. Once you have the pattern down, you can then overlay it on 4/4. The counting over 4 bars would go like this:
1234123412341234 … 1 (Note the single beat 'correction' at the end of the fourth bar)
Your ultimate goal is to be able to count in three or four over longer passages without losing your place. This is a great technique to add to your repertoire and, as alluded to above, it will fit almost anywhere. You can also play the 3 figures in double time or half time to good effect.
(Probably the best book for unpacking this approach is Jim Blackley's "Essence of Jazz", which also covers 3 over 5, 5 over 4, 5 over 3, and more (jimblackley.com).