I cannot remember the last time I did a remodel, or new build where flooring was not involved.  What you put beneath your feet in any space is extremely important.  Flooring can set the mood (warm and cozy in the bedroom or cool and fresh in the kitchen), regulate temperature, create great accoustics or quiet echoes, prevent damage to underlying foundations, keep you dry in case of a flood and even protect you from termites and rodents (yup, I will tell you how!)

Basement Flooring:

There are some very specific and important things to consider when looking at flooring for your basement. 
1.The main purpose for your space:
Games area?
 - You will want something durable and hard
CONSIDER: Vinyl, laminate, stained or etched cement, ceramic tile and bamboo
TV, reading and relaxing?
 - You will want something warm and soft underfoot
CONSIDER: carpet, cork, or engineered hardwood
Office and work area?
 - You will want something durable, hard (to roll chairs), but warm 
CONSIDER: cork, vinyl, laminate, bamboo
Play room?
 - you will want something durable, stain resistant, warm and fun
 CONSIDER: vinyl or rubber (comes in great colours and fun patterns), laminate
 - something warm, soft and cozy
CONSIDER: carpet (unless moisture), vinyl (rich wood look)

Or... perhaps a combination of all the above.

2. Region/area where you live:
A lot of moisture?
 - you will need a flooring that copes well when exposed to water and resists mold
CONSIDER: vinyl, rubber, stained/etched cement
 - dry climates can attract termites that will damage some types of flooring
 - dry climates can encourage cracking and flaking of some floors
CONSIDER: cork, carpet, laminate, vinyl

3. Age of the house and how intact the foundation is:
Cracks in the foundation?
 - you will want to fix these or make sure you are using moisture resistant flooring in case of flooding
Is the foundation poured cement, wood or even dirt?
 - very old homes may be sitting on a wood or dirt foundation and will limit your use of some flooring choices

4. Resale:
Most people I talk to are not looking at turning around and selling their home anytime soon, however, life is unpredictable and you never know when you might be in a position of having to sell your house.  Finishing a basement increases the living area of your house and this could potentially increase the value of your home.  My advice to anyone finishing their basement is: DO NOT cop out and put cheap flooring in because "it is just a basement".  Potential homebuyers have to see this space as an extention of your home and believe that just as much quality and care went into designing this area - you will get your money out and more!