The majority of groups form for a single dungeon run and that's it. Most people solo landscape questing, leves, and so on unless they've got a friend they always group with more for the social aspect than anything else.
The only common exception that gets people to group up for landscape content is FATE grinding. Sometimes people will form parties and just keep going from one FATE to the next. This used to be quite popular as for a while that was considered the fastest way to gain XP. In the 2.1 update, however, SE increased the XP available through dungeons, so not nearly as many FATE grinding parties show up as there used to be. (It's still a really good way of earning XP. It's just that it's no longer the only really good way of earning XP.)
There's a Party Finder feature (found under the Social section of the main menu). There too, however, the majority of people putting groups together are doing so for single dungeon runs, with occasionally a FATE grinding party in there as well. Also, the majority of groups don't use it. (I suspect this has to do with the fact that it wasn't available when the game launched, and by the time it was added people were already used to putting groups together without it.) More often people ask their FC or linkshell if other members want to join them for whatever content they're doing, or people will ask in the /shout channel if anyone wants to join their FATE grinding party.
And there's the Duty Finder, which is exclusively for instanced content like dungeons or guildhests, and for which the game itself can find people to team you up with (which can include players from other servers — whom you couldn't team up with on your own without the Duty Finder). (Having the DF find you a party is optional. You can also form a party yourself and then just use DF to enter the dungeon, or form a partial party and have DF find additional members to complete it.)