If you are on a municipal system and have pressure that high, you quite likely already have a pressure reducing valve (PRV) installed near your water meter. The International Plumbing Code requires PRVs on any water supply over 80psi. If this is the case, your PRV may just need adjustment. As they age, the spring regulating the device's operation can soften. Or it could be faulty and need repair or replacement. If you do not have one, you need to have one installed.
If you are on your own well with a pressure tank, the pressure switch controlling pump off operation needs adjustment. Other types of systems should have similar arrangements to control pressure.
How to adjust a PRV. There is typically a bell shaped housing with an adjustment screw and lock nut on top. Loosen the lock nut and turn the adjuster counter clockwise a small amount. The adjustment can be rather sensitive. Operate the faucets and toilets in your house to allow the system to equalize to the new pressure setting. Take a new pressure reading. How much it changed will give you an idea how much more adjustment is needed. Typical water system pressures should be somewhere in the 40-60 psi range. Shoot for the high 50's.
If the PRV controls supply to a fire sprinkler system (it normally shouldn't), you will need to check with a fire supression professional to determine if and how much you can reduce the supply pressure.
If you do need a new PRV, check with your municipality, they sometimes offer rebates to help mitigate some of the cost.
It's nearly impossible for us to diagnose this without being there in person, but typically wet basements are caused by ground water--rather than a leaky window or the like.
The ground water needs to go somewhere. If the soil can't drain, it builds up pressure and looks for a way into your basement--either via the walls or, more often, where the wall connects to the footer at the floor.
Cheaper/easier things to try first:
- Add/fix gutters and downspouts
- run downspouts further away from house
- properly slope the ground away from the foundation around the house.
- install surface drains (such as a dry river bed)
- have gutters/surface drains go to dry wells
More expensive/complex solutions:
- Install internal footer french drains and a sump pump
- dig down exterior to install exterior footer french drains and waterproof exterior
Fixing gutters and such is fairly inexpensive and a weekend project. Sloping the yard and surface drains are a bit more work, but still in the realm of DIY.
Installing footer drains and waterproofing the exterior below grade, however, is not a DIY project and will cost quite a bit.
Best Answer
There are a few different ways I've seen this done.
The best way is to trench around the outside of the foundation down to the footer, seal the outside of the wall, and install a drainage system (gravel and pipes) at the footer to redirect the water to a sump pit where it can be pumped out.
Next best way is to do basicly the same thing, but on the inside of the house. You bust up the concrete floor of the basement along the walls and install gravel and PVC pipe under the floor to drain the water to a sump pit where it can be pumped out.
Both those options are going to be pretty expensive, and probably not something you would want to tackle on your own. Which is why many people opt to simply seal the inside of the walls with a product like Drylok as Scott mentions. It's pretty effective if you only have minor moisture problems, but if you regularly get lots of water in the basement, it's probably not going to solve your problem.