It's a haworthia, which is a kind of succulent. Eventually someone can probably tell you the particular variety. If you're planning on keeping it in that cup, you'll need to cut drain holes in the bottom.

Hey Joe the Cactus, you're a scream, mate! I dig your sense of humour. My head-count... gee, I dunno I ran out of fingers and toes a long time ago! talking about heads though, don't lose yours mate, remember John did! Pijaya, it's likely you and Larry are right, thanks to you both for the info and your pics!! the filaments on the tips of mine are quite short in comparison... and it's definitely not a Haworthia aristata. Cheers, CP Cheers

friend,go to the propagation forum,alot of great info there.I just cut off a branch about-10-12 in,remove all the lower leaves.I cut an angle right below a node,dip in root tone and put in moist sand.I have one type that self seeds and have to pull them up by the hundreds.I have them planted every where and have alot of pots.Some I just compost.I also do this with hydrangeas,roses and verbenas.I have pretty good success with this method.There are some things that will root in just plain water, moonphase

Oh! Thank you so much. (I had to look up inflorescence.) I'm so glad to start learning some of the terms and what to look out for. I'm glad that you experts work in a little tutoring along with possible identification of the plant. I thought that I might cut it off and try to get it to root closer to the leaves (Is leaves the correct term?). At any rate, thank you for the help. This is going to be such a great hobby. I've loved succulents since I was a child (now, a senior citizen), but until the drought here in California, they weren't considered anything but weird. Now they're the "IN" thing - and getting more expensive by the day. What used to be 59 cents is now 5.99.