This thread comes up fairly high on the subject in the Google rankings (I was actually looking for something else), but there seems to be a lot of confusion.
Quick Summary of Camera Settings
sRGB : Use for Digital display medium such as monitors, phone screens, tablets, web publishing, embedding into video games, etc. (probably 90% of what people do with their photos these days).
AdobeRGB : High-end printing. Requires the proper print driver, print profile and a quality printer, or useful for sending the photo to a professional print shop.
JPEG : Embeds the color-space information. Set the camera up correctly (white balance, sharpness, presets like Portrait or Landscape, exposure, etc.) or suffer the consequences of ruined shots. Does not require further processing on the computer to develop a usable photo file. As a correlation, most additional processing may not be possible.
RAW : Colorspace (and most camera settings) are ignored and stored as mere suggestions for further processing tools. Full control over every detail of the photo, requires time and dedication to process the "RAW" negative into a JPEG. Most mistakes (except ISO, shutterspeed, aperature) can be fixed.
When you set up your Canon for shooting, the first thing to think about is what you will be doing with these photos for the most part. If the photos are intended for presentation on the web, a tablet, your phone, setting the camera up for sRGB is correct. All this does is embeds metadata into the output to tell other software (web browsers, Lightroom, Photoshop, image viewers) how to correctly represent the colors for a digital output medium. As an aside, most laptop displays these days can't even display 85% of the sRGB space and you will need to specifically shop for a high-end laptop to get up over 95%.
On the other hand, if the intended use for the photos will be mostly printing, choosing the AdobeRGB colorspace will set the output up for high-end printing. You will not be able to see these colors accurately on a monitor while working with them on a computer unless you shell out for a high-end graphics monitor, such as the NEC PA241W.
RAW vs JPEG vs Both
Many Wedding and sporting event photographers choose JPEG for two reasons: the camera can capture them and write them to the memory card at much higher rates than their comparatively larger RAW siblings, and when the shoot is done they are much faster to publish, as JPEGs do not require further processing or conversion to look good. JPEG is also the right format for anyone who doesn't have the stamina or dedication it takes to process the RAW "negatives" to generate higher quality output. JPEGS are a good choice for the casual family photographer.
The caveat with JPEG is that you must have your camera white balance set correctly at the time the shot is taken. Over- or under-exposing is fairly permanent in a JPEG (although brightness can be corrected to a degree, but it messes with the colors).
RAW is what I use because I want full control over the entire end-to-end processing of my shots. The settings for JPEG/output now only matter for how the photo is represented by the camera's display (and in thumbnails in some software). You can completely mess up the settings (Faithful vs. Neutral, overly sharp or too much color, etc.) and at the end of the day, it does not affect the RAW file. RAW files are literally RAW because it is a record of all of the raw data the image sensor captured. The camera settings used (like white balance) are also recorded, more as a courtesy, but these can all be changed later. RAW files must be further processed in a program such as Lightroom or Photoshop elements, on a computer that has a Canon RAW driver installed (which tells software how to read the RAW). You can shoot with a Florescent white balance on a sunny day and completely not worry about the mistake. (Shooting JPEG, that's a ruined photo). And you can change the colorspace from sRGB to AdobeRGB and back when working with RAW. The RAW isn't what gets displayed on the monitor or in the print output, it's the processing of the RAW that matters.
A good reason to shoot RAW + JPEG (either consistently or periodically) is in this scenario: you don't want to necessarily spend the time processing the RAW negatives and just want to use the JPEGs shot by the camera. The RAW is there as a backup in case the shot is priceless and you want to do something different than what your camera was setup for.
For example, say you set up your camera for sRGB, Auto white balance, Portrait mode. In general you're taking pictures of your family picnic and most of the shots are of people, so the Portrait mode warms up the skin tones and softens the shot a little. The intended medium is Flickr, so sRGB is correct, otherwise web browsers will display the wrong colors to your fans. Around sunset, you notice amazing light and contrast near a waterfall and you snap off a few shots. But the Portrait mode wasn't a good choice for the images and you definitely want to get this one printed at a professional printing shop to put over the fireplace. Now, you have the option to process the RAW file in Lightroom, set up the colors, change the colorspace to AdobeRGB and send it off to the printer.
Processing RAW for Display
After you're happy with your RAW processing, when you export, choose sRGB for photos that someone is reviewing on their computer or publishing on the web. For example, maybe you're printing a quality photo album of your sister's wedding but before you blow through $400 in ink, you want her to choose from the digital portfolio. If you send her photos exported in the AdobeRGB space, she'll think you hate her. So, export the photos in sRGB. When you've selected the photos for print, export with AdobeRGB, set up the printing profile and print away.
Displaying AdobeRGB accurately
This is the subject of entire books. In a nutshell, you'll need about $1500 to purchase a high-end monitor like the NEC PA210W (I mention this one again because it is well regarded and there aren't too many options out there), which runs about $1000, and a color-correction device like the Colormunki, used to profile both the monitor and print output. The monitor must be calibrated for the light color of the intended viewing environment (eg. 4500K or whatever). The printer's output must match colors on the display almost exactly.
Keep in mind sRGB will print just fine for most general applications. Printer drivers expect people to be shoveling sRGB JPEGs into the printer, so they optimize the colors by usually increasing saturation (which makes detail-oriented people like me freak out; I photographed an asian friend whose skin hue was slightly in the orange spectrum. Their home printer made him look like he had a cheesy fake tan so I really had to dumb down the saturation in Lightroom to get the printer back to where it should have been).
High-end printing is just another matter altogether and takes weeks and months of dedication to learn. I'm still a novice in this particular area and it's a tough learning curve.
I've provided a lot of detail here based on my experience and extensive reading on this stuff. If you're showing your work online in any medium that generates light (screens), sRGB is what you want. MOST people should be shooting in sRGB. It should be noted that the AdobeRGB colorspace can always be converted down to sRGB for display purposes, so it's not the end of the world.
The serious hobbyist, semi-pro and professional photographers who are printing for color accuracy, galleries, magazines, or quality display in the home will want to shoot RAW and post-process. When exporting, choose AdobeRGB and let the professional printshop know that they are setup for this.
I hope this helps anyone looking to understand the colorspace setting of their Canon cameras better.