List of Quests with a level cap.

***UP TO DATE QUESTS WITH A LEVEL CAP***

 World Tours

Movie Star - Under Level 40
***NOTE*** You MUST complete Actor Training, a level 40+ quest, in order to start Movie Star.

 Astaroth Quest Line

Marbas the Demon! - Over Level 18, Under Level 40. (Magician)
Treasure, and Crocell the Demon - Over Level 18, Under Level 40. (Pirate)
Catch Valefor! - Over Level 18, Under Level 40. (Thief)
The Final Battle with Amdusias - Over Level 18, Under Level 40. (Bowman)
Dances with Andras! - Over Level 18, Under Level 40. (Warrior)
For the peace of Victoria Island - Over Level 26, Under Level 40.

 Party Quests

 Sea of Fog

The Rumor in the Sea of Fog - Over Level 90, Under Level 150.

[spoiler=Nett's Pyramid]In Search of the Long Lost Pyramid - Over Level 60, Under Level 89
***NOTE*** You do not need to complete this quest in order to do the PQ if you're level 90-109.

[/spoiler]

 Monster Park

Big Fun in the Monster Park - Over Level 60, Under Level 94
Big Fun in the Monster Park - Over Level 135, Under Level 164

 Chryse

The Floating Island of Chryse - Over Level 50, Under Level 75
This is Chryse? - Over Level 50, Under Level 70
Finding the Village Chief - Over Level 50, Under Level 70
Chief Marione's Second Request - Over Level 50, Under Level 70
A pet? - Over Level 50, Under Level 70
Secret of the Core - Over Level 50, Under Level 70
Chief Titan's Request - Over Level 50, Under Level 70
Xerxes, the Source of the Crisis - Over Level 50, Under Level 70
Qualifications for a Savior (1) - Over Level 50, Under Level 70
Qualifications for a Savior (2) - Over Level 50, Under Level 70
Worried Michaela - Over Level 50, Under Level 70
Obtaining Practice Spears (1) - Over Level 50, Under Level 70
Obtaining Practice Spears (2) - Over Level 50, Under Level 70
Obtaining Practice Shields (1) - Over Level 50, Under Level 70
Obtaining Practice Shields (2) - Over Level 50, Under Level 70
Coliseum Investigations - Over Level 50, Under Level 70
Eliminate the Guards (1) - Over Level 50, Under Level 70
Eliminate the Guards (2) - Over Level 50, Under Level 70
Eliminate Xerxes - Over Level 50, Under Level 70
Please return Xerxes to his former self - Over Level 50, Under Level 70
For the Elder - Over Level 50, Under Level 70
Eliminating Xerxes's Remaining Pests - Over Level 50, Under Level 70

 Maple Alliance

Rise of the Aliance - Over Level 15, Under Level 74
***NOTE*** Completing this quest may skip out on a (few) extra quest(s) from the lvl 75+ version of this quest, such as Cassandra's Prophecy.
***NOTE*** This quest seems to be event-only, and is now disabled.

3/14/2012 Update
-Well, what the hell. Half my post got erased from editing. Whatever. I'll just post a list of current level-restricted quests, then. >_>
-The record of Goddess Minerva no longer has a level cap of 70.
-Sea of Fog's quest may change or be removed in Alliance Unbound.
-Chryse quests added! Quest names may not be 100% accurate. I may or may not be missing quests, as well.

3/17/2012 Update
-Added Alliance quest.
-Sea of Fog quest updated.
-Nett's Pyramid quest added.

3/20/2012 Update
-Corrected the level cap for the Chryse quests.
-Also double-checked the quest names, no mistakes there.

6/29/2012 Update
-"Spiruna's Concern" and "The legend of Papa Pixie" no longer have a level cap of 70.

7/2/2012 Update
-Monster Park quests' level cap updated. Lvl 95-134 without Monster Park is just dumb.