I'm wondering what happens if I don't trim them?

So stem plants die off eventually if I just leave it as is?

No, but they won't look very good. If you don't prune them, they'll block out
the light to other plants by growing over the top of the tank. Some will also
switch to emersed growth, growing up out of the water. This looks nice in a
pond, but in a fishtank, it can be kind of ugly. Once it's growing above the
water, the plant often stops producing leaves underwater, and you end up with
unattractive bare stems in the tank, and all the growth above the waterline.


Leigh

http://www.fortunecity.com/lavender/halloween/881/