Unlike some other OSes that implement the obnoxious out of memory killer or equivalent, Solaris doesn't overcommit memory (unless you are using very specific allocation techniques). When regular memory allocations are made, the OS make sure this memory will be available when required (i.e. reservation). The drawback is you need to have enough virtual memory space to store this potentially partially unused memory.
Free RAM is unrelated but it accounts in virtual memory size too.
Have a look at "swap -s" output when the problem occurs.
Note that you can easily increase the swap area by adding swap files or devices.
Windows and linux have two different page/swap strategies.
Linux
Linux wants to avoid using swap space at all, and waits until the last possible moment. If you see a large amount of swap in linux, your system likely is or was in trouble. This strategy is good for minimizing overall disk i/o, which is the slowest part of your system, but weaker for systems with alternating periods of light and heavy load (and honestly, that's most of us). The times when your load is already heavy will now be burdened by the "extra" disk i/o, or, put another way, you need to design your server builds with an eye to having enough ram you don't swap even during the highest expected load times.
Windows
Windows wants to treat memory as a mere cache of the page file. Your real memory is always on disk, but it will read/write from the "cache" first if it can. This strategy is good for evening out your load over time; when the system gets busy and needs to swap pages, the current page is already on disk and half the work is already done. This approach made huge sense back when Windows was young, 32MB (forget GB) was still a lot of RAM, and the frequent need to use swap space was a given. Even today this is good for work-loads that alternate between light and busy loads, as it helps spread the disk i/o out more evenly over time.
Modern Windows versions have additional optimizations — such as SuperFetch — to pre-load and prepare memory pages on disk and in RAM when the load is otherwise light, to help avoid the need for extra disk writes when loading a program for the first time. All of this means you can design your system to only need enough RAM for something less than the highest expected load, so you can still have at least acceptable performance all the time, with reduced costs.
Convergence
This concept of measuring or predicting load in a test environment first and then allocating production resources when the load is known is a relatively recent development in system building, made possible, or at least practical, in part with the advent of virtual and then cloud servers. Depending on your load, you may even design the system such that it never needs to swap at all. In these cases, Windows does allow you to turn off paging and behave more like a linux system. However, you have to be careful; if your system design requires more memory than expected you can get yourself into trouble this way.
On the other hand, modern linux kernels are more willing to swap to disk opportunistically than they once were. So the difference in memory management strategies between the two systems is still present, but now less distinct than it used to be. Both systems have their merits, and each watches the other to see which advances they can copy.
Best Answer
The swap file is not simply a buffer to run into when you run out of physical RAM. That is an over-simplistic view of how the swap file operates. That said, you can operate without a swap file, as long as you're 100% confident that you'll never exceed your RAM's capacity, at any point in time. Because if you do, your system crashes.
IMO, better to keep the page file and also keep tabs on how often it's being used by the system. If you're never thrashing, it's not a problem, and if you are thrashing, you have an issue that'd probably be even more serious if you weren't running a page file at all.
It's true that we have more RAM now, and it's cheap. But that's also true of disk space. Unless you have a compelling disk space constraint, I'd recommend sticking with a decent size swap file.
If you feel things are being paged to disk too often, you can look at tweaking your swappiness to be less aggressive.