Is it common/wise to invest in multiple flashers for different situations or can you use one given it has enough intensity? Another way to read this is: can a flash be too bright?
You can typically reduce a flash's intensity, either by lowering it's power setting (I have a couple that go to 1/64 their full power), or by adding "neutral density" gels to it. So you can almost always make a flash less bright if necessary.
But it's pretty much impossible to make a single flash brighter.
So, there's usually very little danger in having a flash that's too bright. Most times you'll have the opposite problem.
However, there's lots of other good reasons to have multiple flashes. @mattdm has already mentioned having multiple lights with multiple angles. And occasionally, when you need a lot of light, you'll want multiple bright flashes (usually mounted on some sort of bracket). This is most common when shooting outdoors in full daylight, and you still want to shape your light; you need enough flash to overpower the sun.
For many typical situations, having one (mid- to high-end) flash provides plenty of light in terms of quality, but it's not necessarily where you want it. Take a look at questions here in the lighting-basics tag for some very nice explanations (including diagrams) of some basic portrait-lighting setups, many of which involve multiple light sources.
Another part of your question seems to be about flash power. Almost all modern hotshoe strobe flashes automatically (either through camera control or their own sensors) fire at reduced power when the full discharge isn't required for the exposure. Or, you can set power level manually (to various degrees depending on the exact flash model).
1) Any flash could be too bright if it is too close to your subject, or your camera settings are bad enough for that amount of light. You can blow a photo with a candle light inclusive.
2) You never buy several flashes to have a lot of light! You buy several flashes to controll the light!
One single flash, no matter how powerfull it is will not solve the vast majority of situations... This include the sun itself! Half the day the sunlight is blocked by a big ball.
A total yes.
Outdoors, indoors, small setups, big setups, enormus setups, low key, high key, one light portrait, 2 lights, 3 light portraits, cars, industrial buildings... a concert when everyone fires theyre smartphones... well, you do not own thoose flashes...