Most of the comments are right on about having to get rid of the source of the moisture first, otherwise you will have a permanent battle on your hands. If it is general light mold around the basement and there is no staining from outside water instrusion, then you probably have a general humidity problem. You could check on that by tearing a hole about a foot around in the worst looking spot if it is drywall or panelled - if there is mold smell or black or fuzzy white mold/fungus on the back of the piece you take out, on the studs (or rust or free moisture if metal studs), or mold or dampness on the foundation wall then it is more than just interior humidity - you probably are getting moisture through the wall from outside. This is the most likely case, unless your basement has no circulation with the rest of the house.
Another clue would be if any metal items (pipes, joist nails, etc) in the basement are rusting. Also, if the mold is appearing on spots other surfaces in contact with the outside ground (like interior walls, furnishings, stair risers, ceiling or underside of main floor) then your general humidity is definitely WAY too high, and probably means you either have no ventilation in the basement, or you have leaks through the foundations or around the basement slab.
You locally get a feel for diffusion through wall or slab by temporarily tightly taping a piece of plastic sheeting over a section of the wall or floor - leave it overnight, and if it has noticeable condensation on it the next day you have excessive moisture diffusing into the room from that surface.
You can get a decent humidity gage at a hardware or box store for about $7-10 - if your humidity is over about 70% then you are too damp. What reads as about 70% in the basement room can mean 100% (condensing conditions) at the colder exterior walls.
Stopping actual flowing outside infiltration requires going outside, removing the fill from around the house, and installing a membrane or bitumastic waterproofing system (and possibly drains) around the entire foundation - $10K + typically.
If you think it may just be interior moisture condensing on the colder surfaces, then removing the moisture is the key. If you have exposed concrete or concrete block walls, there are moisture-retardant paints that will limit vapor movement through the foundation. It will NOT stop actual leaks - just moisture diffusing through the foundation from the moist ground outside. There are separate trafficable moisture-control paints for bare concrete floors. A bare floor and wall full-house basement that is wet onthe outside surface can contribute up to 5 gallons of moisture a day to the house - more than enough to cause condensation in the cooler basement. These measures you can do yourself according to the instructions on the cans (after the bleach and scrubbing treatment to kill and remove the existing mold - read up on mold removal techniques and safety on Federal Housing Administration or Cooperative Extension Service websites). You can also buy mold and mildew inhibitor packets to add to the paint at your paint dealer.
Also check if you have any exposed dirt in a connecting crawl space - some houses have a half basement with only a crawl space under the garage and/or family room, and if there is not a tight and effective vapor control barrier over the bare ground then a lot of moisture can get into the basement air from there.
An open sump pump sump with standing water can also contribute a fair amount of moisture - you may beable to cut a piece of plastic to fit over the sump (leaving clearance for the mechanism to operate) to reduce this source - fasten down so it cannot be kicked and block the operation of the float switch mechanism.
Substantial ventilation and/or dehumidification can also remove a fair amount of moisture, but that is an on-going battle. Ventilation should be with low moisture air (inside air - heated if possible, as warm air will collect more moisture when it mixes with the downstairs air) if possible, especially if you live in an area with high summer humidity outside, and the airflow has to be enough, and distributed around the perimeter of the room (large stand-up fan ?), to actually collect the moisture, and then of course it has to be vented to the outside to get rid of the now-moist air.
One solution used in some houses is to duct heater and air conditioner air into the basement as well (which is usually not done in unfinished basements), or to install a "Robin Hood" fan between the main floor and basement, to steal some air from the main house and blow it around in the basement. This is not the best solution, because the return air is vented into the house, so the moisture is not being removed from the house envelope.
All this can be addressed by an energy efficiency consultant, or by an HVAC (HEating, Ventilating, and Air Conditioning) contractor if you don't want to attack it yourself.