I shred and compost leaves and thin diameter flower stalks.

Thicker stalks like Miscanthus, I cut into 1-2" pieces and use them for mulch.

Really big stalks like Sacharrum ravennae, I cut down whole and use like Bamboo, for garden supports and such.

That's a great idea, I have to remember to set aside a few stalks next spring for staking.

I usually take the electric hedge trimmer and starting from the top of the clump go back and forth to get 4-5 inch pieces. These I either rake together and suck up with the lawnmower or I place directly into the compost pile.

A friend of mine burns the clumps as they stand... then cuts down the remaining stubs. It really does a good job cleaning up all the dry fluff that builds up in there and a couple warm days brings the grass right back. Firing up the grass is entertaining but it fires up the neighbors a bit too. Needless to say it doen't happen in my own yard... not on a regular basis at least :)

If left standing until spring, I have found that my large grasses don't burn very well - not enough leaves left. BUT .. those small leafy ones sure do go up in flames quickly - a bit scary that!
We were lucky enough to buy a straw mulching machine at an auction. It does a fabulous job on chopping up all parts of my grasses, leaves, compost, whatever.
A.