There are currently well over 100 untimed and non-event-related quest / goal series in the game. Some do not unlock until a certain number of stars when the cooking station in question also unlocks (like the Sushi Master Station and the three different quest series for that, or the three (or four?) different quests series with the Hofbrau Skillet.
After a special event (Valentine's Day, St. Patrick's Day, Fourth of July...) has expired, sometimes - but not always - Zynga add a new event goal that is not timed, where the goal is to get all stars on the cooking station in question (examples are the Clay Cooker which uses Air Balloon Ribbons instead of stars, the Cursed Cauldron which uses stars, the Patriotic Cooker). Examples of stations that do not leave a quest after the event has ended is the very old Romance Stove (which is still available in the Marketplace, but locked by the "Make Your Move" goals) - if one has it, one can no longer unlock the Intermediate Dishes, due to the "Make Your Move" goals having disappeared - which uses Love Letters instead of stars.