There are may options available for flooring your basement because almost any flooring material will work. However, you need to consider how the basement will be used and determine if the basement will be susceptible to moisture. Of course the more water resistant and durable the material the better.
Stained concrete is one of the cheapest and easiest flooring options. There is a wide range of colors and application techniques available. No specialized tools are needed and it is fairly easy to install. It is also one of the most moisture friendly finishes available. However, stained concrete floors are hard and cold. They also require periodic resealing.
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Laminate floor tiles are relatively inexpensive, easy to install and to remove as your basement needs may change. This flooring is durable, easy to clean and easy on your feet. There are hundreds of design options. Most laminates come with a warranty and some are even certified for basements. The only main disadvantage is that they can not be repaired but have to be replaced.
Rubber flooring is cheap, functional and looks great. It is available in a variety of colors. The flooring is water proof so mold and mildew are not a concern. They are soft and sound absorbent so great for a kids playroom.
Carpet is another viable option for basement flooring. However, it is not recommended if there are any moisture problems. Carpet holds moisture and will mildew if exposed to moisture over time. A big advantage to carpet is that it is fairly inexpensive per square foot. It also makes a room feel warm and is soft to walk upon.
Ceramic tiles can withstand a lot of abuse and traffic. They are easy to clean and hold up to moisture well. It is a best to get tile that are certified for basement use. You can find closeout tiles at your home improvement store and tile distributor that will help to keep the cost down.