Throne Room, like Treasure map and Fool's gold, is a card which works exceptionally well when it combo's and quite mediocrely when it doesn't. Unlike treasure map and fool's gold, however, what throne-room can combine with varies from board to board and is, in general quite a broad range of cards. Also unlike Treasure map and fool's gold, throne room is invariably a bad opening card.
Throne-room is essentially a very weird village with a bonus (or, if you prefer, an of inverse shanty-town with a bonus), if it doesn't hit you are frustrated, if it does hit (it was worth the price.
Note that throne-room applied to even a worthless pearl diver, effectively acts like a village with a moderate bonus (probably one of the stronger 4 cost ones if it was a card) (look at the bottom card of your deck, draw either it or the top 1 + 2 actions). When throne-room hits pawn, you can get a peddler benefit (by choosing +1 action +2 cards, + 1 coin), or use a whole bunch of added flexibility. When throne-room hits a stackable attack (cursers/rabble/noble-brigand/torturer/etc) the end result is stupidly powerful, when throneroom hits a terminal drawer, you can draw an absurd amount of cards. When throneroom hits a good cantrip, you get a village with some very nice extras (for lab you get a level 2 city, for tournament/treasury you get a bazaar). With scheme on the board you can even get a permanent village with endgame explosion potential by constantly top decking throneroom/scheme.
Suffice it to say that if your throneroom hits it is worth it, this implies that if you are going for an engine already, throne room is a good buy once you have a few components ( 3/4 non-throne-room actions is sufficient. ). Now throne-room, like all villages, acts as an engine enabler, if you were already marginal about going for an engine, throne-room makes it worth going for one, village/draw engines gain extra viability when thronerooom is on the board (though they still want either a strong attack or +buy). If there is a stackable attack you can make an engine out of, it is almost certainly worth buying throne-rooms and add them to your engine. A throne roomed witch/mountebank is one of the harshest things in dominion and even the ordinarily maligned noble brigand/saboteur can prove deadly when stacked.
Certain specific cards should immediately make you consider throne room, bridge, which becomes much more potent when stacked, is naturally enhanced by throne room. Scheme can be throne roomed in order to create a permanent extra village per hand or a guaranteed throne room in the endgame. though all attacks benefit from throne room, rabble and torturer, which both offer big draws and are better when stacked are exceptionally fond of it.
Throne-room can be so powerful that certain card are specifically immune from throne-rooms benefits. Haggler, princess, highway, and goons, while all still giving some benefit when throne roomed, all have in play clauses that negate there most potent effects (extra cards, lower prices, extra vp per buy) from being doubled. These cards anti-synergize with throne-room and in general, are not it's best targets (though throne-room can still thrive when used on there support cards)
So when should you not go for throne room? Well, when engine potential is not there. If there are no can-trips present, throne room is nearly always a mistake (very heavy trashing can make it viable). If there is no +buy /strong attack, you should stick to big money X. Throne-room acts as a powerful engine enabler, if there's no reasonable engine to be enabled the high frequency with which you will draw throne-room dead make it not worth your while.
Works with
Stackable attacks
Scheme
Bridge
Minion
Monument
Hunting Party
Talisman (gain extra cheap actions
Engines in general
Conflicts with
Goons
Tournament (a parried tournament is no good when throne-roomed, you are unlikely to have two provinces in hand at a time, and princess/followers are worse when throned)
Haggler
Highway
Fool's gold
Hoard
Militia
Treasure map
Ghost Ship (though being ghost-shipped allows you to move an unusable Throne Room)
Big money games in general