Lots of things can cause that squeek/groan/tick/click/clack, whatever sound it is your crank/bottom bracket/pedal/chainring/chainstay is making.
If you're lazy like I am, trying things that require no disassembly is the place to start. 50% of the time the thing you're hearing is a loose chainring bolt, these are the five bolts that hold your chainrings onto your cranks. They put this funny nut on the backside that requires a special tool, or just nose around until you find some form of flathead screw drive to hold it in place while you tighten the 5mm bolt. Usually you don't have to worry about the backside nut, you'll just need your 5mm Allen wrench.
Next option, take off pedals, smear the axle with grease, replace pedals.
If the noise is still there, take off crankarms, smear the spindle with grease, replace crankarms. This is a little tougher if you don't have the tools and knowhow. Pretty much every garage bike mechanic ruins a set of crankarms in their lifetime because they pull the crankbolt, install the crank puller, and commence pressing off their crankarms without taking out the little crankbolt washer. This will yield you a set of threads you're holding in your hand, and a crankarm that is now both ruined and nigh unto impossible to get off. After you do this you should wear a duncecap for a week (wear it over your helmet while riding). Though no one will admit it, we've all done this (except me of course).
Then there is always the possibility it is the bottom bracket. This seems to be the likely thing when you're riding the bike and hear the noise, but it almost never is. It certainly isn't the cup rocking inside the shell, since there are so many threads holding it in place. It could, however, be the spindle rocking back and forth on inside the cups or the cartridge bearings (depending on whether you have a cartridge or ball bearing bottom bracket). You can tell this by pushing your cranks back and forth with your hands, while the bike is stationary. You'll be able to feel the play. Some frame makers end up with BB shells that are slightly less than 68mm, this is sometimes the reason for such a problem. Some BB's are adjustable for this (such as Real BB's, the ones we use).
Last thing it would likely be (and this is unlikely) is that your crank's square hole is not cut precisely square, and it's rocking back and forth on the spindle. Of course if you have a newer Shimano BB you have a splined BB, and so certainly don't have this problem. I've seen this mis-cut square hole once. The way you can tell is to fixture the bike in your workstand and try to rock the crank back and forth on the spindle, pulling one arm while pushing on another. You'll probably be able to feel a "click" if this is what is happening. As you're rocking it back and forth stop every time you push or pull and spin the crank around the BB, make sure the chainring spins true. If the chainring changes in its trueness as you push or pull laterally on the end of the crankarm, your crank is rocking on the BB spindle.
If it's none of the above, face it, your high is bummed, let me know when you find out what it is so I can add it to the list above.