Hmm, I'm not sure that amplifiers with smaller gain are necessarily more stable, but I think it's often true that large-gain amplifiers will be somewhat unstable... a large gain means that you get a big change at the output for a small change at the input, which means that small effects at the input could make things change a lot. (The specific properties of amplifiers we'll see depend on solid state physics; we'll cover this later in a bit more detail.)
In our practical applications though, negative feedback for amplifiers is ubiquitous. We'll pretty much always be using devices that either have negative feedback built in to a package (so it's invisible to you, the user), or else if you are making an amplifier from ``scratch'' (i.e., from op-amps) you will nearly always use some kind of feedback circuit.