Can trees grow without sunlight?

Trees can definitely be grown underground with sufficient light. According to this thread on the Minecraft Forums, you need 7 blocks of space above the sapling. (Perhaps this condition isn't being satisfied.)

7 blocks of height is required.

A neat trick is to put stone next to the saplings, so you don't have tons of leaves that you have to deal with.

from above, this is what I do:

XXXXXXXX
SXSXSXSX

XSXSXSXS
XXXXXXXX

S <- Sapling X <- Rock

Note, the Sapling has to be planted in dirt. Put torches on the rock pillars to light the saplings,and you are good to go!

Any light will work for trees. However, you may need more space.

My underground (automatic >:D) tree farm is 200x200, for the trees at least, and I've found trees require at least 1 block on all sides, and at least 7 blocks up. I have it at 10 right now, but to get the bigger trees you'll have to expand it to around 20-30. To get large jungle trees, you need around 60 blocks space, and yes, I have done this before.