I believe the previous answers address only a small part of the problem.
First, there is the issue of hardware. It does us no good to know that we have an OS capable of using up to 192GB, if the expansion slots can only accommodate an extra 4GB, for instance. So here the issue is: how do I know how much more memory can I physically add?
Here the answer can only be: you will have to look it up. It is essentially a matter which every producer (Dell, Acer, Lenovo, Sony, Toshiba,...) addresses on the basis of (among other things) marketing strategies (is this pc going to be top of the line? basic product? intermediate?). Reasonable rules of thumb are that desktops will have larger and more expandable RAMs than laptops (big surprise...), that it is uncommon to find laptops exceeding 8GB (but some do exist), that typical gaming pcs have of order 32GB, but there are so many exceptions that the value of these rules of thumb is limited at best.
The second reason why previous answers were incomplete is that they only address Windows pcs, while of course there are Macs as well. Here the situation is much simpler because of the smaller number of models to which this question applies. You can find the complete list of maximum amount of RAM for each Apple product since G3 here. The list is however still sufficiently long that it is impractical to reproduce it here. But let me just say it is very complete.
The third reason why the previous answers were incomplete is that, even from the point of view of software, the maximum amount of RAM that an OS can use depends on the OS. For instance, let me give you the limits of the Linux Kernel:
32 Bit - 4GiB RAM
32 Bit + PAE (Physical Address Extension) - 64GiB RAM
64 Bit - 2^32 GiB ~ 4 billion GiBs.
As you can see, there are here two major differences with respect to Windows. On the one hand, there is an important modification of the 32-bit kernels (PAE) which allows even these to take advantage of amounts of RAM exceeding the (naive) theoretical limit of 4GB for 32bit machines. On the other hand, there is a huge limit to the amount of addressable RAM for the 64bit version, that makes it suitable even for the largest machines currently available: Titan has 693.6 TiB of RAM spread out across 18,688 nodes (GPU RAM accounts for about 1/6th of that). This incidentally, jibes with the fact that all supercomputers (except 1) use OSes of the *Nix family (see the statistics here).