Euphorbia milii 
Family - Euphorbiaceae

There are so many species of Euphorbia and they range from bushy shrubs to leafless cacti-like creatures.
Here is my experience with the one that is - Euphorbia milii. This plant strikes you with it's exotic and at the same time cheerful appearance. If put at the right spot - it will be blooming all year long. Where is the right spot?
From my experience - south facing window is perfect. Don't be afraid to put euphorbia under direct sunlight. More sun it gets - brighter the flowers color will be. Educated botanists just about now would say that the bright colored roundish bracts are not actually flowers but leaves around unnoticeable little flowers. Well, they do look pretty anyway.
Usually euphorbias continuously loose their bottom leaves, so they have bare trunk with bunches of leaves at the ends of branches. It is normal for old-fashioned euphorbias. Lately new hybrids of Euphorbia milii came out on the market. They don't loose the bottom leaves and grow into nice looking bush sprinkled with bright-colored flowers(yes I know they are not flowers). I noticed that this type of Euphorbias need a bit more watering, otherwise it will loose the leaves too.
It is quite tricky to propagate Euphorbias with cuttings. First you need to dry up the cutting for couple of days, then pot it into moist sand + peat moss mixture. And here comes the dificcult part: you must keep the potting mixture just a little moist but not too wet. The catch is - if too wet - the cutting will rot before rooting, if too dry - it will never root. If you are lucky and will get it right - in 5-8 weeks the roots should develop. When repotting Euphorbia add coarse sand or perlite to the soil mixture, it likes good draining soil.

Here is the picture of the little euphorbia milii hybrid that doesn't loose it's leaves. It is sitting on the south facing window, getting a lot of sun, so the color is much brighter then the one above - big one.