I have a tube fluorescent fixture in my kitchen (it's actually those U-shaped tubes) that takes a long time to start. If you flip the switch on, it will either not do anything, or part of a tube will light dimly. After several minutes (or after you slap the side of the fixture) it will come on to full brightness. What would cause this?

What ballast type it uses?
If it is RS, the cause would be bad contact on some pin (likely "coated" with wet and oily dirt from cooking fumes), so the lamp does not heat up.
The kicking then make the contact for a while, so the lamp start. When running, only one contact on each end is enough to maintain the operation (and even if it is not as good, the arcing clean it out), but for starting all contacts have to work correctly even at low voltage (so without the arcing cleanup).
So i would suggest to disassemble the fixture, clean all connection (or replace sockets, if this would not be possible)...

There is a cover over the ballast(s) so I can't tell at the moment. The bulbs however are Philips FB40CW6EW. I believe that's a T12 Rapid-Start?

If it never flashed at startup, it is likely the RS.
But even with preheat, if the starter connection is loose, it may behave in similar way: Kicking on the fixture make temporary contact, that in fact start the lamp...
Other reason for bad starting may be dirty tube: If the tube has resistive surface, it lower the field around electrodes, making it harder to start (grid field effect).
So still I guess, then inspecting, cleaning and fixing connections in the unit should solve the problem...

It also could be a bad ground.  I've often seen this happen with a rapid start fixture that was not grounded.  Touching the fixture actually "grounds" it, which causes it to start up.

It also could be a bad ground.  I've often seen this happen with a rapid start fixture that was not grounded.  Touching the fixture actually "grounds" it, which causes it to start up.

I should note that the fixture doesn't always start up when you hit it, but how would you diagnose a bad ground? I will examine the fixture tomorrow and clean the contacts.

Just check the wiring inside the ballast channel.  All rapid start ballasts should have a green "ground" wire coming out of them in addition to the wires which lead to the lampholders and the hot (black) and white (neutral) wires.

Check to ensure that the green wire is adequately connected to either a green wire or a copper, unsheathed wire coming into the fixture from the junction box.  If the green wire coming out of the ballast isn't connected to anything, that's your problem right there.  You should then go ahead and connect the green wire to the ground wire in the junction box.  (You will probably have to loosen the fixture from its mount to be able to access the junction box).

If your house wiring is old (pre-1960), there may not be a ground wire present in the junction box.  In that case, you're kinda stuck with a slow-starting fixture.

Of course, make sure you shut off the current at the circuit breaker before touching ANY wiring in the fixture!  I don't mean to sound patronizing, but...SAFETY FIRST!  

Rapid start T12 U-tubes are notoriously temperamental.  In this case, if what was suggested above fails, I'd consider converting to an electronic T8 setup.  If it's a light you often turn on and leave on for a while, an instant start ballast is fairly easy to find and will do the job.  If you turn it on and off frequently, go to an electrical supply shop and spend the little bit of extra money to get programmed start ballasts.  They are much easier on the lamps when starting, which will make a difference in life when frequently switched.
Either way will be more reliable and less temperamental than the rapid start U-tubes.

If your installation does not contain the PE connection, you may connect the shield to the Neutral via Y-rated (see UL rating on the component) safety capacitor (these are intended as RF suppression for switching converters, you may found them in electronic wall AC/DC adapters). These components are assumed as "insulation" from safety point of view (leakage current <1mA on the mains voltage, fail-open only), but provide strong enough "connection" for the lamp to start (require few 10's of uA only)

Other option would be to put 5x 220kOhm/0.5W resistors in series into transparent heat shrink tube and connect the shield to the neutral via this string. The tube should be transparent, as it should be clear, then it is not a wire (or otherwise somebody would later try to "repair" this "broken wire" by the real one, connecting the shield directly to the neutral, making a safety risk...)

time to upgrade.had several of those that were very tempermental.humidity up?no start.line voltage a tad low in the summer?same.
got worse with new low mercury tubes.refitted with 4 f17t8 and a electronic ballast.the cutouts were already there.overkill.since i have solar and a huge battery bank i removed the 4 lamp ballast and put in a 2 lamp driving only 2 tubes.put in a 1 lamp 24v dc ballast to take care of the other tubes.it is rated for up to a 6'tube so it runs 2 2' in series.works great that way.had to run a dc line and switch but it was worth it.

You mentioned that the lamps are "EW"...This is the 34 watt "Econ-O-Watt" version of the F40 tube.  Try a new pair of FB40T12/CW/6 lamps and it should work MUCH better.  The 34 watt versions of U-bent lamps REALLY suck.  F40s are much better.  I converted a U-bent fixture to preheat, just for the helluvit!   Here is a video of it.  Very reliable starts this way!
http://www.youtube.com/watch?v=yGGkTCuVMkM

Good to know. Unfortunately, I don't have any new or old U-tubes for the fixture, so I can't compare to the existing tubes. I did clean out the contacts on the lamp holders, but it didn't have any affect on it. I did examine the fixture though: It's a Lithonia fixture with a Regent ballast (didn't know they made ballasts). It's probably from the 1980's. All of the wiring appeared to be intact. The fixture will likely be replaced in a year or two, but it would be nice to have it working in the mean time. 

You didn't mention whether or not the ballast was "high power factor".  This could play a role in the problem you are having with that fixture as well.  NPF (normal power factor) rapid start ballasts are notoriously problematic.

You didn't mention whether or not the ballast was "high power factor".  This could play a role in the problem you are having with that fixture as well.  NPF (normal power factor) rapid start ballasts are notoriously problematic.

I'm pretty sure it's high power factor (can't remember exactly, I looked at it over the weekend). I can double-check tomorrow.

Changed out the ballast with a known working one, and same thing. Cleaned the contacts on the tombstones with contact cleaner, and no difference. Thinking it's time to replace the lamps.