The first thing you have to do is realize that there may be multiple noise sources, and if you bring in your bike to have a mechanic check it out, don't get too annoyed when he or she starts finding various things that you're positively sure are not the noises you were hearing. You have to take things one step at a time and rule out everything you can.
Now for a few basics.
#1: Noises frequently sound like they're coming from someplace other than their actual source. This is because just about any metal under tension tends to be an excellent transmitter of noise and vibration, and this would include such things as chains, spokes and even the frame itself if it's metal. Carbon fiber frames act as a resonator adding to the difficulty of assessing the exact source of the noise.
#2: Many noises aren't even coming from the bike, but rather accessories that are attached to the bike. The #1 non-bike source of noise is the interface between a cleated shoe (the type that click into the pedals) and the pedal. Whether it's LOOK, Speedplay, or SPD, this can be a definite source of noise, which is why our mechanics will frequently ask that you bring in your shoes along with your bike.
#3: When describing noises, you need to categorize them as either high-frequency "clicks" or low-frequency "clunks." This is very important, since they indicate very different potential noise sources! Also note whether you actually feel something happening or just hear it.
#4: Keep in mind that noises are not always an indication of impending trouble. The rear cassette (or freewheel on older bikes) will vary in loudness through its life...in general, being somewhat noisier when new and quieter as they age (and the internal parts become a bit less violent in their springiness). One of the best addages to keep in mind when thinking about noises is "if it ain't broke, don't fix it"!
Now we're ready to take things on one at a time!
Handlebar, especially where the brake levers attach to it! This is extremely common, on new bikes as well as old. Keep in mind that the handlebar is constantly flexing and, especially on road bikes, the part that the lever mounts on is a veritable noise-magnet. The easiest way to tell if this is a noise source is to try flexing the bars around and listening for noise, and then loosen the screws that hold the brake levers to the bar and try again. If the noise is still there with the levers loose, then that's not likely the source. When re-tightening, make sure the threads on the bolts are lubed!
Stem. Make sure the binder bolt that tightens the handlebar to the stem is well-lubed and tight. Also, pull out the stem and grease the surfaces of the wedge that tightens the stem into the frame, and especially be certain the you grease the underside of the allen bolts, since that interface itself can be a source of noise. It can sometimes help to put a thin layer of grease on the part of the stem that grips the handlebar, especially if it's a take-apart stem (one with a removable face plate).
STI Road Bike brake levers. While this mostly applies only to '98 and later Ultegra and '99 and later 105 equipment, it's a big enough issue that it bears mentioning here. Those little plastic nameplates on the front of the levers are nuisance when it comes to noises! They are held on with a screw behind the name plate, and if that screw comes loose, those things will rattle enough to drive you crazy! The covers themselves can also rattle due to age and be a similar problem. To remedy this, simply pry off the name plate (be careful; they do break fairly easily and that little piece of plastic will run you about $8 if you break it!), check to be sure the screw behind the plastic is snug, and apply a bit of silicone adhesive to the top and bottom of the name plate. Pop it back into place and you're ready to ride!
Cranks. Check to make sure that not only are your chainring bolts (the four or five bolts that hold the chainring to the crank) tight, but that they are lubed as well. This means backing them out, one at a time, and applying either a very heavy oil (Pedros SynLube, for example) or a lightweight grease (just about anything marketed for bikes) to both the threaded surfaces of the nut & bolt as well as the areas where they contact the chainrings. Also, especially if you're using aluminum chainring bolts , check them carefully to make sure they haven't developed cracks. They will fail eventually (aluminum just isn't strong enough for long life in this application) and, prior to completely breaking, they will make pretty severe ticking noises.
It's also a good idea to remove the crank arms and be sure somebody didn't apply a bunch of grease to the flats...this is usually not recommended, since the crank's machined surfaces will "ride" on the grease instead of making strong contact with the bottom bracket spindle, and this will rapidly accelerate wear of the mating surfaces. The exception is that splined bottom bracket spindles DO require lubrication with grease or, even better, anti-seize compound.
Bottom brackets. With the advent of cartridge-bearing bottom brackets, noise problems are more common here than ever before. Two things are going on...first, you have a design where your bearings are sitting in a cartridge, and that cartridge sits on top of the axle. Problem is, the axle flexes, changing the amount of contact between it and the bearing, which causes clicking noises. The other problem that shows up with cartridge bottom brackets comes from the interface between the cartridge shell and its bearing. This problem can sometimes be alleviated by removing the bearing from the shell and using anti-seize compounds on the contact points.
Wheels. Some noises that are apparently from the bottom bracket area can actually be coming from the wheels. Front quick releases are often the culprit, and lubrication of the system and/or tightening of the quick release can alleviate the problem. There was an issue with some early versions of Rolf wheels where the axle end cap moved enough in the hub axle to cause a clicking noise. The combination of that noise and an OCLV carbon frame...boy, THAT noise sure sounded like a bottom bracket issue!
Another wheel noise is one that comes from the unloading and reloading of spoke tension as the wheel rotates under the stresses of riding. This can usually be overcome by the proper tensioning of the wheel itself.
Spoke reflectors can be another cause of wheel noise, especially if it comes and goes as you go through corners. Make sure the reflector is solidly wedged into the spokes (which usually requires sliding it up towards the rim as far as it will go).
Saddles. A BIG source of noise trouble, and frequently saddle noises will mimic crank noises since both tend to occur at the exact same frequency (same part of the pedal stroke). Sometimes the noises occur from the saddle rail/seatpost interface, in which case you should disassemble the seatpost, grease all threaded surfaces and the underside of the head of each bolt, and reassemble. Rarely, the noise comes from the part of the rail that goes into the saddle itself. We haven't found a permanent cure for this, but putting some oil into the affected areas helps for awhile.
Freewheels. Unless you have a single-speed track bike, your bike has gears and a freewheel in the back that allows your wheel to move while your pedals remain stationary. We call this "freewheeling"...in the old days it was simply coasting.
The method used to allow this involve ratchets in the rear wheel mechanism...a very simple device that allows for free movement in only one direction, allowing you to either coast or pedal without needing to engage any levers etc. These ratchets are very much like what you'd find in any tool set, and when you spin them, they make noise, usually at the rate of about 18 or so clicks per revolution of the wheel. In some designs, the ratchets are quite noisy, either because they're located closer to the outside of the hub mechanism, or because they're extra-strong. In other hubs, these ratchets are very quiet, perhaps because they're located further inboard or packed in heavier grease.
Often, a freewheel that started its life fairly quietly will become noisier over time, and this is rarely cause for concern. In general, a noisy ratchet is a happy ratchet, provided that you don't notice it binding if you try to turn it by hand. Please note also that the tone of the noise can change depending upon what gear you're in, even when you're not pedaling. This is because the chain is exerting a pull from one side of the rear cogs or the other, depending upon what gear it's sitting on, and this affects how the bearings and ratchets are carrying their load. This is perfectly normal.
Indeed, the scariest of freewheels is one that has suddenly decided to go quiet. This may be an indication of ratchet failure or near-failure (there are two different ratchets in each freewheel, so one can fail and the freewheel will still function for a time), and it would be wise to bring the bike in to the shop to get checked out.