Basements can certainly pose some challenges when you're planning to install some flooring over your concrete, challenges that center around one sometimes illusive, sometimes irritating, potentially destructive element to every basement: moisture.
Carpet, not considered especially-green, and hardwoods are typically not the way to go in a basement scenario. If you think moisture's a problem, try mold. You certainly don't want to invite mold in your home by using carpeting in any area that might see significant amounts of moisture. And with hardwood floors, though they are beautiful and functional, wood and water have a pretty rocky relationship as well.
What about cork? Cork is definitely a possibility for basement installations, but because almost any product can be damaged by consistent exposure to moisture, there are some things you need to do to get the best out of your basement-relegated cork. First, you need to determine if the moisture content of your basement is within range to have any type of flooring other than paint applied to it. If you have significant moisture problems, then you definitely need to get them corrected before starting on a flooring project. No matter what type of flooring you choose, if you don't, you will have problems down the road. Once you've tested and established that your floor can tolerate some covering, you'll need to consult professionals about the ins and outs of installing cork flooring in a below-grade environment.
Though cork can tolerate moisture better than hardwoods, it's still wood and is not impervious to water's destructive nuances, so you'll need to use a moisture barrier under your cork flooring. You'll also want to seal your tiles after installation to keep moisture from penetrating. Look for a polyurethane sealant that is water-based and has low VOCs; three to four coats may be needed to fully seal the tiles themselves as well as the cracks between them. You can use a beeswax-based protectant, which is super green, but it might not give you the same level of protection as the other type of sealants.
Last, but not least, you don't want to install any kind of glued down installation in a basement setting. Moisture is glue's most hated enemy because it sure wears it down quickly. So if you go with cork, be sure to choose a floating floor installation and not a glue down.
There are some other options out there, but cork, with its resiliency, durability, and interesting expansion qualities, as well as its premier "green" product status is a good bet for a basement.