Your question is a little too narrow for my tastes. Some of the best cheap purchases that I've made are things that I still have now. They haven't worn out or broken or become useless.
In 2001 I bought a new cast iron fry pan for $20 that I use on regular basis and it's marvelous. Around the same time, I bought some used silverware from a thrift store and I still use that everyday.
Two other purchases that go back more than 20 years are my pocket knife and my 1/4 inch hex driver, both of which I bought new but were not particularly expensive and they are working wonderfully to this very day.