A brief, highly simplified reply:
sRGB is the lowest common denominator. If you want utmost simplicity, use sRGB for everything.
There are a few monitors that will display more than sRGB, but many only display sRGB. Most web browsers will assume sRGB no matter what tag the file has, so if you look at an Adobe RGB file it will look dull.
Many online printers ignore the profile and print as sRGB.
sRGB will probably lose some of the colours your camera (or scanned film) is capable of producing, and it will lose a lot of the colours an inkjet printer can print (especially dark blue-greens and light green-yellows). An inkjet printer may not be able to reproduce all the purer blues and greens that are in the sRGB space, however.
sRGB and Adobe RGB have a similar gamut in the purer blues (so the sRGB-printer and Adobe RGB-printer mismatches are about the same), but Adobe RGB has a wider gamut in the purer greens, so the mismatch between Adobe RGB and the printer gamut is usually greatest there (compared to the sRGB-printer mismatch). Adobe RGB may, however, be very close to the printer gamut in the mid tone yellow-greens. (Remember that a basic inkjet printer uses cyan, magenta and yellow inks, so pure greens and blues have to be made from a combination of inks. The yellow is usually quite pure, the cyan and magenta are not as pure spectrally. Thus pure, saturated blues are a big problem without a blue ink)
Adobe RGB (1998) is a larger colour space, but it can't be displayed on most monitors. More and more monitors are appearing that are exceeding the sRGB gamut.
If you are interested I'll post a few graphs showing some of the stuff I've mentioned.
Edit:
ProPhoto RGB is a very large colour space. Too large to be well represented by 8 bits per channel, so 16 bits per channel is recommended.
I use Adobe RGB as my working space, and convert to sRGB for output if necessary.
Best,
Helen