It depends on the game. For example, in ToT, there's a series of quests you can complete to bring back the Harvest Goddess. However, you can play your farm and not do any of them, and after I did beat them I kept playing because it doesn't end the game. Most of them are kind of like that. At some point, if you have a kid, they can inherit the farm from you too. But I've never played that long because I have a short attention span.

I got Harvest Moon Grand Bazaar for the DS last Xmas but then my DS broke (before I could really play it).I would highly recommend Rune Factory 3 though. It's a "fantasy harvest moon" so you have the farming piece (plus armor, accessories, and herbal/medicine stuff), wooing the ladies in the town, plus a fighting aspect. You can adopt monsters to work in your fields too. I actually played it through twice, I liked it so much.