One of the advantages of using an electric guitar connected up to an amplifier is that you can use a mind-bogglingly wide range of devices which can do almost any conceivable thing with your sound. They can be in floor-mounted 'stompbox' or rack-mounted units, depending on your setup. Below is a general list of what the major types of FX boxes do, and the links on the left link to the major manufacturers.
Distortion
One of the most popular types of effect is the distortion unit. The precise definitions vary, but generally a distortion unit makes your guitar sound louder and/or creates a distortion to your sound which adds sustain, texture and colour to your sound. Overdrive pedals are designed to mimic the harmonic distortion that results from a cranked amplifier, but at a controllable volume. Such pedals include the Boss OD-2, the Marshall Bluesbreaker II and the Mesa/Boogie Bottle Rocket. Fuzz pedals create a more harsh and static-sounding distortion, which sounds somewhat unlike amp distortion; these were popular in the 60s and 70s and are still widely-used today. Famous fuzz pedals include the Fender Blender, MXR Fuzz Face and the legendary Electro-Harmonix Big Muff Pi. I personally like the sound of the Big Muff, but I also use a Pro Co Rat 2 for a more overdrive-like sound. The mild overdrive of the Bluesbreaker II is pleasant enough, but there are pedals that give a more modern, heavy metal sound (such as the Boss HM-1 Metal Zone) if that's your thing.
Phasers, flangers and choruses
Although I have lumped them in the same category because their circuitry is fairly similar, phasers, flangers and choruses have very individual sounds. Chorus pedals are fairly self-explanatory: they give the sound of two or more instruments being played at once. This is usually done by the pedal copying the signal and altering things such as pitch or timing to give two or more slightly different sounds. Chorus pedals are very useful for getting the sound of a twelve-string guitar out of a six-stringed instrument; they also give a very pleasant warbling ambience to the sound. The Boss CE-3, Electro-Harmonix Small Clone and Danelectro Cool Cat are some of the most famous chous pedals in use. Kurt Cobain was a big fan of using a Small Clone, which produces a very watery, analogue kind of sound. Phasers alter the amount of treble and bass that passes through over time, giving an affect that sounds like a wah pedal being rocked back and forth. The hypnotic, cyclic wah-wah bass line of Pink Floyd's 'Sheep', the opening guitar line of 'Have a Cigar' or the intro to 'Mayonaise' by the Smashing Pumpkins are good examples of an Electro-Harmonix Small Stone phaser in action. They can also give a whooshing effect, which leads me onto the flanger effect. This is like an over-the top chorus, giving a more metallic whooshing sound. Originally, flanging was created by playing two copies of the same track on separate tape machines, and altering the speed of one tape by pressing on the 'flange' of the reel with a finger or thumb (incidentally, this technique is still occasionally used in the studio). Fortunately, your guitar sound can be given the same treatment by connecting it up to a flanger pedal (such as the Boss BF-3), which can adjust the speed, depth and prominence of the effect.
Echoes and Delays
Echo units are another effect type which does exactly what it says on the tin: they create an effect which produces a single echo to what is played. Delay pedals do the same thing, but have the added advantage of being able to produce two or more echoes. This can be used to give a chorus-like effect of the time setting is set low, or can give very spaced-out ambient effects. A delay pedal can also be used to give a rhythmic texture to a guitar line; there are some parts on Pink Floyd's 'The Wall' in which delays are used to give a 'galloping' type effect which makes it sound as if the guitarist is strumming faster than he really is. Reverb pedals are designed to give a 'spacey' vibe by creating many echoes, allowing you to have a very atmospheric sound without having to use your amp in the bathroom or something. Many guitar amps already have spring reverb built in, but it isn't to everyone's taste.
Other Effects
Of course, the above effects are just some of the stomp-boxes available. Wah pedals (as used by a bloke called Jimi Hendrix - you may have heard of him) are brilliant for spicing up a lead passage; compressors 'smooth out' a guitar signal, making loud parts quieter and quiet parts louder for a more constant volume; harmonizers (this classiication includes octave dividers) take a note that is played and generate additional note(s) of a pitch that can be set by the twiddle of a knob or click of a switch. Personally, I'd love to get my hands on a harmonizer unit, because it creates an impression of two or more guitars played at once. Unfortunately, the circuitry that can generate different pitches is extremely complicated, leading to an inevitable increase in price. An interesting variant of the harmonizer is the 'whammy' pedal made by Digitech. It has a wah-pedal looking treadle built into it, which allows the relative volume of the original note and the harmony to be altered (when in harmonizer mode) or can be used to raise or lower the pitch of the note (when in whammy mode). In other words, as well as being a harmonizer which allows you to mix the original note and the harmony, it also mimics the sound of a tremolo arm being moved by rocking the treadle back and forth. The crazy pitch bending of Tom Morello and Billy Corgan are good examples of how cool this pedal can sound. The Boss PS-5 Super Shifter can do a similar job, at a slightly lower (but still rather high) price.
I hope that gives you some idea of what those coloured metal boxes that guitarists stamp on actually do. The best thing to do is of course to try out a few in your local guitar equipment shop. The individual sounds of different brands can vary enormously, as can the price. In case anyone is interested, my pedal setup is:
Pro-Co Rat 2->Electro-Harmonix Big Muff Pi->E-H Small Stone->Boss CE-3 Chorus->Boss DD-5 Digital Delay->Boss BF-3 Flanger