totally depends.
If you need a tech, or if getting that tech before anyone else will get you something (like another GP), then that's often a good idea. However, I've found that the tech they'll give often isn't the one I would want, so I usually pass on this option.
Great scientists are great for Academies, especially early in the game. Otherwise, I'd save them for golden ages. Rarely, to join a city.
Great Artists are essential to join cities when going for a cultural victory, or at the end of the game to culture bomb my 3rd-lowest city to bring it up with my first two.
When not going for a cultural, GAs are great for culture bombing a newly captured city, or a city which is losing to a neighbor's culture pressure.
Great Merchants are sometimes good for the gold. Often I use them to get a tech. Most of the time, though, I use them to join my biggest finance city. Since they give food, plus gold (which benefits from all my gold buildings like Bank), they're awesome there.
Great Engineers are the best. Always, always, save them to get wonders.
Wodan