Regular Maintenance
Regurlarly maintaining your vehicle is something that you should be doing anyways. It won't actually make your car go faster per se, but it will prevent it from going slower.

Premium Gasoline
Fuel that is of a higher octane tends to burn better than the cheaper gas, and ends up giving off more energy than lower quality fuels. Premium will actually make your car run faster and better.

Spark Plugs
A modern combustion engine needs three main things to run: fuel, oxygen and a ignition(spark plugs). Higher quality spark plugs will improve thecombustion of the engine, improving power. You can buy all kinds of spark plugs including one made with platinum and even iridium. These plugs perform considerably better than the factory ones that came with your car when you bought it.

Cold Air Intake
As mentioned, one of the main components of a combustion engine is oxygen. If you replace your engine’s stock air intake with a more efficient aftermarket cold air intake, airflow to the engine will be improved, increasing performance. The only drawback is that some of that quietness for power and fuel efficiency.

Exhaust System
Not only do cars need to inhale oxygen, but they also need to exhale. So just like the factory intake that came with your car, the exhaust system is designed to run quietly. Switching your exhaust system with wider tubing and a freer flowing muffler will improve your car's ability to exhale.

Nitrous Oxide
Please understand that nitrous oxide can be very dangerous, but at the same time, super awesome. This is a gas that if improperly used, it can actually cause your engine to literally explode. Nitrous basically works as though it's extra oxygen in your engine. The result is that it makes the car work harder and go faster.  However, it also increases the pressure in the engines cylinders, this can actually cause you engine to explode. You also use up nitrous as you use it, and at a very quick rate, so it's something you have to replace every once in awhile.

Turbo Charger/Super Charger
These are often stock components, but can always be added on as an aftermarket part.  They are also much safer than using something like nitrous. Turbo chargers and super chargers both basically work the same. In a nutshell, they are air compressors that push more oxygen into the engine than there usually is. This increased amount of oxygen allows the engine to burn more fuel at a faster rate. The increased amount of fuel transforms into increased power and thus speed.  The main difference between the two is that a super charger is available immediately when you hit the gas, whereas a turbo charger only kicks in once you reach a certain number of RPMs.

Swapping out the engine
This is hands down the most expensive modification you could do to your car. Basically, it's putting in an engine that's way more powerful than the stock engine that came with your car. You could get it from a bigger car, or buy a brand new engine that isn't even made for your car. Swapping out the engine can be extremely expensive and time consuming because generally a lot of modifications need to be made to both the engine and the car to make everything fit.