The box of crayons you're given for displaying photos on the web is called sRGB.
There are other color spaces, such as Adobe RGB (1998), but no Windows-based browser can display them correctly. The Macintosh browsers Safari and Internet Explorer can, but only under conditions not normally found in everyday browsing.
To your right you see the same photo displayed in sRGB (above) and Adobe 98 (below). You'll notice the Adobe version is washed out. There is no way around this problem other than to convert your photo to sRGB.
Isn't Adobe bigger?
JPEG files are 8-bit, which means you get 256 reds, 256 blues, and 256 greens whether you use Adobe 98 or sRGB.
However, Adobe 98 is broader, meaning it spreads its crayons across a broader range of colors by making the jump between each color more coarse.
You get finer increments of skin tone by using sRGB, for example. But the pure cyan in HP's original logo can only be accurately represented by Adobe 98, whereas in sRGB you would have to pick a substitute color.
The best (and shortest) explanation of these tradeoffs is here.
What's best for printing?
That depends on both the photo and the printer.
The printers in most commercial labs, such as WHCC (one of our labs), Bay Photo (one of our labs), Mpix, EZ Prints (yep, another lab of ours), Shutterfly (whom we used to use), Kodak, Fujifilm, Photobox, Costco, Snapfish, Wolfe's, etc., shine light on photographic paper, similar to the way film prints are made. They have similar color range to the sRGB color space. Most of them expect your file to be in sRGB and if it isn't, your prints will look washed out.
Ink jet printers, however, spray ink on paper and can represent a broader range of color.
Most consumers judge prints by pleasing skin tones, shadow detail, and the vibrancy of photos—as opposed to the absolute accuracy of a particular green or blue.
That's why the vast majority of us look at stunning photos on the Internet and say, "Wow!"
Very few people aside from high-end color experts notice that photos displayed in web browsers are limited by how many colors they can display.
Get on with the answer, already...
If you have a photo with colors that fall outside the sRGB range that are important to render accurately, and you have an ink-jet printer that can render them, Adobe 98 is a better choice than sRGB (and ProPhoto is even better).
Adobe 98 is also better if you have a commercial client, such as a magazine, that requests it in Adobe 98.
But for most photos of people printed at commercial printers, sRGB is a better choice. And if you want them to display well on the Internet, it's the only choice.
Yikes! What colors do I give up?
You probably didn't notice, but the photo top right has many colors outside the range of both Adobe 98 and sRGB that a Canon 20D was able to capture. The colors that fall outside of Adobe 98 are shown by gray dots, right. There would be even more gray dots for sRGB.
The reason we don't notice is programs like Photoshop are very good at color substitution. When Photoshop encounters colors that sRGB cannot render, it picks other colors which look surprisingly good.
When SmugMug receives non-sRGB photos, what do you do?
We learned from hard experience to convert CMYK, Adobe 98, and ProPhoto images to sRGB. Otherwise they look bad both online and in print, benefitting no one.
So what's the best workflow?
Your camera captures images in RAW. Many high-end cameras give the choice of converting, in-camera, to Adobe RGB or sRGB before saving on a memory card. Sometimes it's written that the best workflow is to save your photos in Adobe RGB because it preserves the most colors, and convert to sRGB for the Internet.
The problem with that is you get the disadvantages of both color spaces with the advantages of neither.
If sRGB covers the colors of your shots (as it does for weddings, portraits, and most event photography) and your shots are destined for the Internet and commercial printers, we recommend they not pass through Adobe RGB first.
Some color experts fume about sRGB. Why?
The last thing a self-respecting color expert wants is to give up colors.
They want monitors and printers that hit every color perfectly, and ICC profiles attached to each image.
But the power of the Internet is its simplicity. The Internet works on TV and TV on the Internet. Consumer devices like cell phones and TVs don't know about ICC profiles and neither do consumer websites like CNN and eBay. They do know sRGB.
Fortunately, 99.9% of us think photos look gorgeous on the Internet, and it flourishes because of the simplicity of assuming every file is in sRGB.