Most of us are computer enthusiasts, and as such we often have quite a few computers.
But usually it is not necessary.
With that said, I do think 2 computers - a desktop and a laptop are the sweet spot.
Desktop - for performance, storage and long-term reliability (easier to fix/replace parts, easier to upgrade, usually cheaper too).
Laptop - for traveling, for taking your work with you, for going between home and office (unless the workplace issues you a company PC, then it may not be necessary to take it with you).
Which laptop - depends on your work style. If you travel a lot and do simple things while on the road, a small light machine is probably better; if you need to do serious computations or regularly work with applications requiring large screen space - a bigger machine with a higher resolution screen may be better for you.
For that purpose, pianowizard's poll about resolution vs portability can be quite informative:viewtopic.php?f=58&t=103968
Now, in some cases it is possible to get by with one machine. For example if you never need to travel with your work, and never need a computer on the road (because you have a tablet/smartphone for those small things) - then you can get by with just a desktop or a desktop replacement laptop.
If you want to avoid the desktop, it's possible to get powerful desktop replacement machines, which can compete performance-wise and storage-wise, but they will be very big, very heavy, very expensive. Not good for portability, unless you like chugging 5 kilos with you everywhere you go (if you drive everywhere it matters less).