The leaves remind me of some kind of ficus, but beyond that I can tell you nothing.

I was thinking it looked like a magnolia, are the leaves fuzzy at all on the bottom

It looks almost tropical but if it was outdoors that rules out any tropical plant. Whereabout are you from? We can try to narrow out the kind of flora that will survive outdoors in your area

Ianna

I live in Vancouver, BC, Canada. I can think of two possibilities: Sour cherry and cantaloupe. I have a sour cherry tree whose leaves looks like this. The reason I suspect it may be cantaloupe because I once drop some cantaloupe seeds at the soil where the plant came out. But I don't know what cantaloupe plant looks like. Can some one tell if this unknow plant is one of them (or some other things)? Thanks!

Cantaloupes are vines like melons or cukes. The leaves look a bit large for a cherry. I would still guess magnolia especially in Vancouver area. They are spring bloomers so they generally have time for the pods to mature. Dead leaves from it are very stiff and do not break down very fast. If it is it should start to bloom within the next couple years.

No such thing as a cantaloupe tree. I'm inclined to think it's a magnolia but you've had this tree for 2-3 years. have you ever noticed it bloom in spring?

Ianna

Looks like bay leaves. Likely hardy depending on where in Vancouver area you are....if it is Laurus nobilis. Check out the link and see if description fits.
Flora

Here is a link that might be useful: bay leaf tree

No, not bay laurel. I have the plant and it's different from the picture shown above.

However, flora - you've provided a clue. There is something called bay magnolia which is a form of magnolia and resembles a bay tree. Native to southern states - heres a link...http://www.yorkcounty.gov/WISE/images/Sweet%20Bay%20Magnolia.jpg

Looks close but only time will tell.