Car goes into neutral while driving

if the transmission is automatic, the most likely problem is low transmission fluid.  If the fluid level is normal on the dipstick, the fluid flow is being restricted.  have the transmission diagnosed by one of the major transmission shops. Most of them will do this for free in hopes to get you repair business.  the transmission probably needs to be flushed, have the filter replaced and refilled.

Though I've never heard of a Honda Corolla (are you sure it's not a Toyota) I will assume that it is a stick shift. You didn't say in which gears this happened but there may be play (looseness) in the shift linkage or something like a bunched up floor mat might be interfering with the motion of the stick. Otherwise its time to check out your local junk yards for another tranny.