Well, some bikes have just one gear...
I have two bikes I use regularly. My Brompton has 3 gears. That is fine for me to get around town with - but, I am reasonably fit, and I need to stand up on the pedals to get up somewhere like Market Street or Dundas Street. So someone else might find that the bottom gear isn't low (easy) enough for them. The Brompton's gears are all hidden inside the hub of the back wheel.
My road bike has 9 little spikey wheels for the chain at the back (my apologies if I'm being over simplistic) - this is called a 9 speed cassette - and two bigger spikey wheels for the chain at the pedals (a double chainring). In theory that is 9 x 2 = 18 gears. However there's an overlap between some of the combinations of front and back, so in reality I don't have that many different gears. The easiest (lowest) gear is still reasonably high, so again I have to work quite hard on hills. However my top gear is much bigger than on the Brompton, so I can go a lot faster.
Lots of bikes have three spikey wheels at the pedals, a triple chainring. This gives you gears that are easier to turn, so that while I'm having to stand on my pedals and work quite hard to get up a hill, someone with a triple can sit and turn the pedals with less effort. Mountain bikes and bikes for touring, which are designed to carry more weight, often have triples.
The other difference between my road bike and Brompton gears is that there is quite a difference between the Brompton ones, so there's a bit of a jump in effort when you change. On the road bike the differences are much less (mostly - it is possible to get it wrong) so my pedalling effort should be much smoother. The other side to this is that I'll be tweaking at my gears a lot of the time, to get the best one, while with the Brompton I touch the gears much less.
So the answer to "How many gears do I need?" is "It depends what you want to do"!
Sorry, that turned into a bit of an essay... hope it helps.