Looks like Dendrobium orchid, and I'd guess kingianum. Make sure there isn't any water sitting in that saucer the pot's in. When watering make sure all water runs out, but don't let the plant dry out completely. It may need repotting, the bottom of that pot looks like it has a heavy build up of salts and the inside of the pot may be the same. These are epiphytes so if you repot use an orchid mix that's very open and airy. Don't know which climate you're in so, they don't mind a bit of cool in winter but definitely not freezing.

Syngonium(Arrowhead Plant)

Wow! Thank you all for getting to me so quickly! Grenda: those look fantastic! I agree, initially I bought the plant because of how it caught my eye at the store. It was like a purple blue-ish (pearlescent) if that makes any sense, just stunning. I can see you have leaves attached to your stems, when I bought mine there weren't any, maybe a sign of something from the beginning. It looked like at one time there were leaves all the way down similar to yours. Chucker: that does look very similar! I wouldn't be surprised if it was some sort of hybrid or not a true succulent. Or it could be that I dont know what I am doing and I am torturing the poor plant. Rina: I am also from Ontario, specifically Ottawa, and I will re pot my plant on your advice. It seems to me that the stuff the plant came in looks a bit earthy. If you're located in Ottawa, what store do you recommend to go to for new soil. So, the plant looked like it did in the first picture for a while after I got it. But then I started to notice that the center of the plant started to go bright green (like the colour in the second picture). The green started to bleed outwards from the center to the outside making it look like it does in the second photo. Generally speaking, it could be over watered or under watered or not enough sun. I doubt that it has too much sun. I was also wondering if I was right by assuming it only blooms once a year? Thank you all once again, this is very exciting and interesting.

If that pot doesn't have drain holes your new plant will need one that does. Also with indoor succulents in particular there is a chronic problem with ordinary rooms not having adequate light. If you can't put this one near a sunny window that isn't curtained most of the time you may have to set up an artificial light source for it to be near.