Un-insulated basements are typically damp, cool and disagreeable places. Insulation can make them a lot more comfortable and useable.
Without proper levels of insulation, even if there are no leakage paths, heat will flow through the construction materials in the walls and floors, increasing the heating (and the cooling) costs, and making the basement and the house uncomfortable places.
Basement insulation doesn't eliminate structural sources of moisture, and problems involving the foundation. These problems should be fixed before the insulation is fitted.
Besides, insulation also makes the walls warmer, eliminating many condensation problems.
When not to insulate the interior of basement walls
Be aware, anyway. If there is signs of water in your basement, if you are having outdoor drainage problems, if your foundation walls are not properly sealed and waterproofed, do not insulate your basement. Fix its problems first.
If there is water seeping through the walls and signs of moisture, do not insulate your basement. Mold, mildew and condensation will be aggravated.
Also do not insulate your basement without sealing it first. Cracks in the walls, and holes and gaps in service penetrations or in the sills and back and deck floor should be properly sealed before installing any insulation.
Traditional methods of interior basement insulation
It's common to insulate the basement walls by building a framed wall against the foundation, and by filling it with fiberglass batts or a similar insulation material, and by covering the frame and the batts with drywall.
This method should only be used in very dry basements, without moisture and water condensation problems, and requires the use of un-faced insulation. Do not forget this last detail; unfaced batts give the moist air an opportunity to escape.
Insulating the basement walls with Polystyrene Foams
Be careful, anyway. Avoid fiberglass batts if there is a significant risk of infiltration of moist indoor air through walls (a real risk in many homes). That’s a direct recipe for mold and condensation problems.
There is a better choice than fiberglass batts: sheets of polystyrene (XLS) foam, attached to the foundation walls. Like fiberglass batts, XLS foam needs to be protected with drywall (or other covering, like cement tile backer board; cement board is more expensive but is mold-unfriendly, contrary to drywall).
Install at least 2 inches of extruded polystyrene, for an insulation value of R-10. In order to achieve a better insulation - which is highly recommended in colder climates - you can add fiberglass batts to the polystyrene sheets (always keeping the foam board against the wall); to that effect you may use 1x3 vertical furring strips to hold the XPS in place and to provide a base for attaching the drywall.
Also do not forget to hold the bottom end of the drywall one inch above the floor, to prevent water ground wicking.
Stone and concrete foundation basement walls
If you have stone-rubble masonry foundation walls, use sprayed polyurethane instead of fiberglass or extruded polystyrene. The foam is sprayed between and behind a frame wall, built against the foundation.
This method requires professional application. See for more technical details: OEE Basement insulation methods