If you know your fuel filter is squeaky clean and your car is still about as easy to move as a narcoleptic elephant, you might want to check your fuel pump. When you hit the gas, your fuel pump is supposed to pump fuel (shocking, we know) to the engine. If it isn't working, your engine isn't getting the fuel it needs and won't respond like it should.
Most cars today use an electric fuel pump (but if your car has a carbureted engine, it will likely have a mechanical fuel pump). There are two types of electric fuel pumps: suction type and pusher-type. True to their name, sucker-type fuel pumps suck fuel from the tank by creating a vacuum. Pusher-type pumps are placed in a car's gas tank and push gas to the engine. They should really try to make these pump names less complex.
Unlike a fuel filter, fuel pump problems are harder to fix. You're probably going to need to take your car to a mechanic, and oftentimes the only solution to a bad fuel pump is to replace it. But, considering that your fuel pump is the mechanism that delivers the food to your engine's waiting mouth, replacement is worth it. Even if your car runs with decreased engine response due to a faulty fuel pump, it's probably just a matter of time before that fuel pump fully shuffles off its mortal coil, stranding you somewhere you'd rather not be.