GFCI's are a very good thing to have, but are not absolutely necessary. For many years, they didn't make them, and people kept aquariums. IF you have kids/other pets, you should put one in however as a safety.
You just have to be careful, install drip loops and never touch electrical contacts, or let water get near them.
Over the years, building codes have changed, which is why in newer homes you have them in your kitchen and bathroom. Old houses typically do not have them, unless they've been remodeled.
In lieu of a GFCI, you can buy, or make, a grounding probe. This is basically a wire with a piece of stainless steel (or some other non-corrisive metal) that sits in the tank and runs to an outlet. It "grounds" any stray voltage you may have so you don't get a shock and your aquarium life doesn't feel any shock.