Why do my RPMs shoot up when I try to accelerate my car?

Basically, if I try to give my can hardly any gas at all, the RPMs fly up, and the car does not respond accordingly. The car will still drive, but the acceleration is horrible. Eventually, the RPMs will level out if I maintain a certain speed, but as soon as I try to go faster, the Rpms fly up again, until I maintain a certain speed.

I drive a standard, and I have taken good care of it (fluid changes, do not race the car, ect). No waning lights are on, and there is only about 75,000 miles on the car. The problem started recently, and all of the sudden, and it tends to be worse in higher gears, but still effects the lower gears.