Are there penalties for dying in FFXIV?

Solution 1:

By default, getting KO'd in FFXIV:ARR means that you get a small durability hit against your gear first. Any spells/abilities/status changes are also removed (So Protect or class abilities will need to be recasted again [NOTE 1]), but any Food Effects on you will stay active. There's no other permanent damage done against your character much like EXP loss in FFXI.

While KO'd, you can choose to return to your home point for free, or wait for a revive. (there's no "time till HP" like in FFXI). If you're in a Duty (Instanced Dungeon or Leve), you can chose to return to the start of the map. (In an instanced dungeon, a shortcut is created after every large boss). This doesn't cost too much beside running time, but if you "return to start" in the middle of event battle (One where walls are created to block people from running away) then you cannot return to that battlefield until the battle is concluded. (Either the rest of the party falls or the boss is taken down.

If you accept a revive while KO'd, you'll return with a 1 minute "Weakness" debuff that reduces all of your stats by 15%. (Max HP/Max MP/and physical stats like STR and MND)

If you happen to get KO'd while under the weakness Debuff, then "Brink of Death" will be applied when you're revived again. (This replaces the "Weakness" debuff from here on out.) Brink of Death reduces all of your stats by 30% for 1 minute, and getting KO'd while under Brink of Death will just reapply the same debuff over again. (So if you have 30 seconds left on BoD and get KO'd again, the BoD debuff goes back to 60 seconds on reviving)

Once either debuff expires, your stats return back to normal. Likewise, getting KO'd again will only afflict weakness again as that debuff chain has been broken.

Edit: [Note 1] In a recent update (patch 2.3?) the abilities Shield Oath and Defiance will not be lost on being KO'd. These constant abilities are used by the Paladin and Warrior Jobs in order to enhance their stats for taking on the Tanking role. As you can guess, whenever a tank gets KO'd and raided without their tanking buff, they're stuck in a very underpowered situation to get the control of the fight again.

Solution 2:

Depends on where you die. If you die in the overworld, you either wait for someone to resurrect you, which inflict a 3 minute stat penalty debuff, or return your aethryte point, which can be really far away. If you die in a dungeon, you have the same option of being resurrected, or you can return the dungeon's starting point, necessitating a long walk back.

Other than that, they are no penalties for dying.