Is it really true that getting sick builds up your immune system or is it better to be healthy and not get sick?

It is true that: Exposure to infectious illnesses can be helpful. For example, teachers often develop immunity to common viral illnesses after years in the classroom.

Only in early life: That is the hygiene hypothesis theory as to why allergic problems are on the rise in westernized societies. Only applies to the early years of life when the immune system is developing.