Yes you can, and however much you want. I believe air-layering is the usual recommendation, but if you're not interested in propagating the plant, all you have to do is saw through it. New growth will emerge -- eventually -- from the new top of the cane, though until it gets itself back up to speed, the plant will use water much more slowly than you're used to, so you will have to be sure to cut back on water. Getting the plant in as bright a light as you can manage, up to and including dappled or filtered sun, may speed the process up.

(Also, if you're not interested in propagating it, consider offering all or part of the old top of the plant for trade or postage on the exchange page. Dracaena canes aren't just falling out of trucks, you know.)

If you *are* interested in propagating it, either air-layer, which is probably better in the long run but might be a long wait (around 8 weeks), or cut the top completely off the plant and then use it to create stem and cane cuttings. It's also not out of the realm of possibility that sticking the top directly into water and waiting might result in your plant rooting in water, though there's more of a risk of losing the top that way. In any case, the base will, again, generate new growth on its own, but you have to watch out for overwatering and get it in bright light if you can.

Cane cuttings:
http://www.ces.ncsu.edu/depts/hort/hil/hil-8700.html
http://www.urbanext.uiuc.edu/houseplants/propagation_cuttings.html

Air layering:
http://www.urbanext.uiuc.edu/houseplants/propagation_airlayer.html
http://aggie-horticulture.tamu.edu/extension/ornamentals/airlayer/airlayer.html

yes you can cut the top off. it will grow more so i'd urge you to cut it into much shorter sections, keeping track ot "up & down" as tjis is very important to the plant.

i find air layering to be a lot of trouble, much more than its worth. just get rooting hotomone & get to work.

cut the cane, dip bottom ends into water & the into roting horomone. place directly into dirt, mounding up a little hill to help support itselt & wait.

pretty soon you'll see new growth wherever you cut the plant.

good luck w/ the new babies, lil.

If it's only bumping the ceiling a little bit, you can grab the center "spear" and pull it straight up and out, removing the top cluster of leaves. That can give you several inches of clearance. Repeat every year or so as needed.

what if your corn plant is top heavy and doesn't have more than 6 leaves?