I like to use at least one Great Merchant for a trade mission--usually the one I get from discovering Economics first. Yes, it's usually easier and cheaper to build new units than upgrade old ones.
However, the Economics GM usually comes along just before I can build Riflemen and Grenadiers--
neither of which can get City Raider promotions, which only become available again when you get Tanks. So I like to upgrade several Macemen or even Axemen with those promotions to preserve that very useful advantage.
Early Great Prophets are great for popping techs like Theology, Civil Service, and Divine Right, and for Shrines--though if I found/capture several religions, I rarely build the shrines for all of them. Later GPs usually become super-specialists in my best commerce city.
Great Scientists are wonderfully versatile. If Taoism has not been founded, I'll pop one for Philosophy, which is also a pre-req for Liberalism and its free tech. Other GS will build academies, pop a tech if it's strategically beneficial, or become super-specialists in a science city. A very late GS almost always gets used for a tech, since the contributions from an Academy or superspecialist are going to be too short-lived to be worthwhile.
Great Engineers are for Wonder-building. UNLESS you're Industrious, because you can already build Wonders quickly and may want to use them as super-specialists in production cities. I confess I haven't tried this before, but some people have suggested it in
my current ALC game as Qin, so I'm going to give it a shot.
Great Artists get stockpiled for culture bombs where needed.
The only time I'll burn GPs for a Golden Age is for a production/commerce boost during the space race.