WOWT reports that at 2:30am, Friday, July 10, an Omaha man was beaten and robbed while cycling on the Keystone Trail near 68th and Q.
Personally, I wouldn't ride any trail during these hours (technically, these trails are operated as "parks" and are subject to hours of operation), but would rather ride the streets. With street riding, there are more eyes out, plus a cyclist has more opportunities for escape routes should the situation turn foul.
Just remember, if you are riding the streets at night, you need lights to see by, and more importantly, to be seen by. It's also the law in Nebraska to have a forward facing white light if you ride at night.
View Keystone Trail Robbery, 2009-07-10 in a larger map