Liam,
Barometric altimeters work just fine. They're also fairly inexpensive.
As aircraft complexity increases, barometric altimetry is supplemented by the input from air data computers; this is standard for aircraft operating in reduced vertical separation airspace (RVSM). At low altitudes, radar or radio altimetry is also utilized.
For a light airplane doing every day run-of-the-mill kind of flying, a simple barometric altimeter works just fine.