When composing, I tend to try to avoid writing rhythms that sit "on" the beat. I instead will write rhythms that move around the beat. This is difficult to explain without showing you in person, but an attempt is worth it.
One way I look at this... is when the rhythm sits on the beat, there's no real tension adding/release.
Say you have in 4/4 time, B = Bass/Kick drum, S = Snare:
1 |2 |3 |4 <<<<Beats
B-2-3-4-|S-6-7-8-|B-10-11-12-|S-14-15-16.
It's when you add rhythmic hits around the beat or skip beats that tension is introduced and you resolve it by landing back on the beat. Say this for example:
1 |2 |3 |4 <<<<Beats
B-2-3-B-|S-6-7-8-|9-10-B-12-|S-14-15-16.
That's for rhythms. You can invert the concept to create really cool stuff. Have the rhythm stay on the beat, but have the melodies, chords etc... using the concept above to flow around the beat and resolve tension by landing on the beat. Practice this, and your songwriting will improve exponentially. Hopefully that was clear because it's an important concept in songwriting in my opinion.
