Seriously, it is possible to (sort of) turn your Hyundai Excel or other asian econobox into a race car. With a few hundred dollars and some work, you can make it hold its own against low-end Mustangs! These modifications are written mainly for 4-cyl. econoboxes with owners on a tight budget. A much different situation applies for muscle cars and those who have thousands to spend.
Econoboxes tend to have quite good high-end torque and a high specific power rating. Because of the high-end torque, however, the power can only be fully utilized in the high RPM ranges. Thinner tires on the drive wheels (in this case, the front wheels), increase the effective gear ratio, which not only increases torque, but puts the engine into the high RPM's quicker. Thinner tires on all four wheels can help improve handling, as well as increasing torque. You can probably get a set of two thin tires for 13-inch rims for $100 or so.
Nitrous oxide provides a cheap and easy-to-install boost for any car. Nitrous oxide is rated in horsepower shots, which is the approximate gain in horsepower for the system. For a 4-cyl. econobox, a 50-hp shot is sufficient and safe. If you know what you are doing, a 100-hp shot can be used, provided the ignition timing is properly retarded, high octane fuel is used, and the fuel system is upgraded to handle the extra fuel (if the nitrous system is a "dry" system).
Weight reduction costs nothing, and will improve handling, fuel consumption, and make your car faster. You can probably save 100 pounds on an econobox by removing the extra seats (don't worry--they can be put back in later), cleaning out the trunk, and removing any big stereo systems and rice boy stuff, which really just adds weight, nothing else.
High performance air filters can provide a cheap, albeit small, boost in horsepower, by increasing airflow. They cost around $50, and there are two brand names--Holley and K&N. The former seems to be better.
Makeshift ram air induction is a virtually free way to provide another slight boost in horsepower. Not only does ram air utilize colder, denser air, the air is delivered at slightly above atmospheric pressure, increasing volumetric efficiency. Just cut an opening in your hood, put a mailbox without a door on top of it,attach the intake hose to the opening, and seal any gaps. The mailbox will collect the colder air, and "ram" it into the intake hose.