My clock and odometer lights are out in my 4 door1999 Honda Accord EX. Does anyone have any advise for me?

Check the fuses. It should say in your owners manual which they are. You might end up having to replace the blubs, it will take a bit of work to get to them if you end up having to.

if the illumination isn't working....i would first check for the fuse like whumba said...but if that's ok....most likely the BCM (body control module) has gone out. if you look up underneath the driver side knee bolster...you'll see a blue box attached to the back side of the fuse panel. you'll have to remove the whole fuse panel to make it easier to replace. just make sure to disconnect the battery first...and have your radio code in hand afterwards.