There are many advantages to citruses that are good keepers on the tree: Longer fruit decoration on display, Perfect storage is on the tree, you will save volume estate in your fridge, Good keepers usually have better taste and are sweeter or have fuller flavor, and when it comes to selling off these fruits, a longer period of harvest means that you cannot be forced to harvest, or you can harvest when there are workers, have a lot better scheduling at your disposal. There are some disadvantages though such as longer exposure to thieves, birds, rodents, as well as the elements which can cause some fruit scalding, or even splitting of fruits due to sudden changes.

Amongst the sample that I know, here are good keepers on the tree from my personal observations (if the fruits really made it that far without being harvested by kids):
Vainiglia Sanguigno
Gold Nugget Mandarin (can stay for 6 months)
Ortanique Tangor
Star Ruby Grapefruit
Mato Buntan Pummelo
Chironja Grapefruit Hybrid

Anybody care to share their experiences?

Here's more good keepers according to this online book:
http://books.google.com/books?id=wz44AAAAIAAJ&pg=PA213&lpg=PA213&dq=citrus+%22good+keeper%22&source=web&ots=VbpoTRJVee&sig=_bJVGfSNjz8POf7NUDNOKQ8rARg#PPA214,M1

Late Valencia
Lisbon Lemon
Eureka Lemon
Agnes Lemon

I forgot to list the Variegated Eureka Lemon which I think is even a better keeper than the regular Eureka lemon.
I also forgot about the Ponderosa Lemon, it is a very good keeper too.

This kind of information is hard to come by from the many citrus books and literature that I have searched, so that is why I posted this, hoping that others will chime in.

To help qualify what makes a good keeper let us tentatively define them to be citrus fruits whose quality (primarily flavor, texture) will not degrade very much when left on the tree for at least 2 months, from the very first time they become ready for use ie, as fresh eating or juicing.

Joe,
In Arizona, we can keep Red Blush Grapefruit, or Marsh Grapefruit on the trees from first harvest in late December until the end of May. Seville Sour Oranges are good for at least four months, but will hang on the trees the entire year if left alone. They simply dry up.

Thanks for the very detailed info Patrick!

The longest hanging citrus fruit that I am aware of is the Myrtle Leaf Orange. Because of the length that the fruit remains on the tree, the Myrtle Leaf Orange, makes an exceptionally ornamental tree, for the patio. The taste of the fruit is so-so. - Millet

Thanks Millet!

I have also observed that sometimes my Valencias and Mandarinquat would last more than a year on the trees before they rot away and fall off. After turning deeper color in the cold winter months, they would turn slightly green towards the spring and summer, but then the taste is on the drier bitter side if left more than 4 months. I wouldn't say they would be decorative when they revert back with some green coloration, so couldn't classify them as clearly as good keepers, more like depending on what other details you would consider. Come winter again, they would turn dark orange then fall off and rot.

This is the same case with Calamondins and most fortunella hybrids. They indeed become decorative for a very long time on the tree, but the peak taste quality that I want with Calamondin, is just when they are turning color from dark green till they are yellow green. Once they become orange to dark orange, they lose their zesty and tart flavors, and while decorative, they lost their flavor quality for most of our recipes. They can still be used for juicing, making wines, marmalades though. But their flavor quality is about 6 weeks on the tree, much shorter if the batch of green fruits start to turn color during the cooler months, like just 2 weeks. But the fruits can stay for up to 9 months before they fall off.

Navelina is known to be good keeping for at least 2 months. Much better than Washington Navels which are only good to 3 weeks in my yard. The Cara cara would be good for 7 weeks on the tree, so a lot better than the Washington Navels. The Owari Satsumas would stay only for about two weeks after reaching their peak flavor, then they would become mushy or rot away due to the very wet winter.

Keep the info coming people! At least from personal observations.

Reading various UC publications, I learned that the following mandarins:
Shasta Gold holds well for 5-6 months
Tahoe Gold holds well for 4-5 months
Yosemite Gold holds well for 4-5 months

Some safe generalizations (there are exceptions of course!):

Most pummelos and grapefruits, once they ripen, and excepting prolonged freezing temperatures, will hold on the tree very well.

All cultivars of Valencia Oranges holds well on the tree.

Kumquats, Calamondins and their hybrids keep well on the tree.

Melogold holds longer by a month than its sister Oro Blanco.

From other various reading, here are the Mandarins that hold well on the tree:

Tango
Fremont
Encore
Kishu
Pixie
Algerian
Kinnow
Honey
Oneco
Page

Still other cultivars that hold well on the tree:

Lane Late Navel Orange
Umatilla (incorrectly 'Umatilla Tangelo')
Minneola Tangelo (a.k.a. Honeybell)
Sampson tangelo (Dancy x unnamed grapefruit)

From: http://www.citrusvariety.ucr.edu/citrus/cocktail.html

Cocktail is actually a hybrid of Siamese Sweet pummelo and Frua mandarin. The cross was made at Riverside, possibly in the 1950s. The variety was never officially released by the University of California, Riverside, but somehow made it into the public sector.

Characteristics: Cocktail trees are large and vigorous. The fruit can vary from the size of an orange to the size of a grapefruit. It has a thin, smooth, yellow rind. The flesh is seedy, yellow-orange in color, and exceptionally juicy. The flavor is pleasantly sub-acid. Cocktail matures in early winter and the fruits hold well on the tree, puffing when they become very old, but not desiccating.