What are you looking at? Last year’s poinsettia of course. Are you surprised? I know that no one really keeps these things from year to year. By March, they are toast–or perhaps if they’re lucky, compost.
But they do have a long and storied history as shrubs, particularly in Mexico, which is their home country. And obviously, if they are growing as shrubs in the ground, no one is doing the crazy machinations we hear about in the news or on blogs or web sites (which you won’t read about here, by the way) about putting the plants in closets or under boxes to get them to bloom. I think those folks who have them as shrubs in their yards have better things to do with their time.
So if you don’t mind your plants not blooming not quite on schedule (and you know I don’t–I’m the one with last year’s amaryllis in June!) this is what you can expect. And this is just the beginning.
So this year, if you have the room, perhaps consider saving over a lovely poinsettia of your own. Or at least compost it, if you can!
Gardendaze 
In the mildest climates, they do somewhat well outside. There were quite a few around the old homes in downtown San Luis Obispo, where I went to school. My great grandmother grew one for many years off the porch of her home in Sunnyvale. They are not very pretty if they get overgrown, but can be restored if pruned down after bloom.
The way you describe them makes them sound like some of our old, over-grown rhododendrons. You should see some of those monstrosities! Some of them can get up to the roofs of second story homes! But with enough time and patience, even those can be renovated. Most people won’t try, however. They’ll just rip them out and start over.
Karla