Other recent MMOs such as Warhammer Online and Guild Wars 2 have embraced the idea of public quests and events, and Final Fantasy XIV is no different. Here, they're called Fates, and anybody in the vicinity can join in, provided they're not too high a level. If you outlevel content, the game will scale your level and stats down appropriately, but it's not as smoothly implemented as Guild Wars 2's scaling system. Some Fates are as simple as fending off waves of enemies in a town, but others (much like Guild Wars 2) chain into larger encounters and sometimes gigantic outdoor bosses.
If you're looking for more to do beyond the regular story quests, NPCs called Levemetes exist in each zone and dole out challenge quests (called Guildleves) to whoever stops by. I haven't run into any that are particularly interesting on their own, but when you begin one you have the option of scaling up the difficulty. The amount of time it takes to complete a Guildleve is finite, and the more time you have remaining at the end, the better your reward will be. Bumping up the difficulty also helps gain greater rewards. If slaughtering things for the Adventurer's Guild isn't your thing, there are also options to partake in crafting and gathering challenges.
Levemetes also hand out group leves called Guildhests - which are one of the most brilliant pieces of content I've seen added to an MMO. Guildhests are short, group-focused challenges that help train you for encounters you might find in the instanced dungeons. If you pay attention, you'll be taught the entire group battle mechanic, and hopefully it helps players understand their role a lot sooner than the endgame.
Instanced dungeons are called Raids here, and oddly enough, the party size is four - usually in games of this type you roll with five players, but what the hell. Let's be different. Some dungeons are actually part of the game's main storyline, and you'll be forced to participate if you want to proceed. As expected, they're littered with trash mobs and boss-class creatures, but there's a little more exploration involved.
In the first dungeon alone, you'll have to find some secret passages and get keys to certain doorways by exploring alternate rooms to proceed. Once you make it to the final boss it's a significantly greater challenge than the standard tank & spank encounter you usually find early on in an MMO. In this case, the boss needs to be held in check by a tank, and the rest of the players need to constantly interact with parts of the environment to prevent extra enemies from joining in. The next dungeon I partook was even more of a challenge, with a boss that summons friends who make him invulnerable to damage.
Final Fantasy XIV's guilds are called "Free Companies". Joining one is usually a good idea when playing an MMO, and membership includes several perks, including permanent bonuses to XP accrual, access to the Company Chest for central storage, and of course, the companionship of your fellow players.
You can also join up to eight Linkshells, which are basically chat rooms for players who may or may not be in the same Free Company. It can get a little weird managing discussions that flow between your Free Company chat and various Linkshells, but thankfully you can designate separate chat tabs in the UI to help sort things out.
To be perfectly frank, I did not expect to like A Realm Reborn as much as I do. While my early preview of it at E3 was promising, the history of the game made me extremely wary. It looks amazing, the soundtrack is wonderful, and there's a ton to do. I've been loving my playtime with it so far, and I might even play this one beyond the trial month, which is about the highest praise I can give to a subscription-based MMO these days.