Firefox and Internet Explorer and other web browsers are actually probably some of the "biggest" programs on your computer, as far as resource usage goes.
While other programs may take up more space on your hard drive, modern web browsers will generally start with more than 100MB system memory (RAM) and go up very quickly from there. A Firefox session with 20 tabs open for days on end will often be using more than 1Gigabyte of system memory.
For comparison, Microsoft Excel, which takes hundreds of megabytes of space on your hard drive, uses only just around 15 megabytes of memory no matter how big the spreadsheet you have open.
Unless you're running a sophisticated audio/video program or a massive database, the web browsers will probably be the most resource-intensive programs you run.
Regarding crashing: your system usually hangs because it has encountered an error, not because it has run out of resources.
For instance, if you have a bad memory chip and Firefox or Internet Explorer, while opening, try to address that bad memory, the entire computer is likely to lock and fail.
However, Windows is pretty smart and should be able to tell you if a particular piece of hardware is causing the crashes.
I would recommend testing your computer memory using a tool such as Memtest x86 or similar if you experience frequent unexplained crashes.
Another possibility is a driver. Drivers are perhaps the most common cause of operating system crashes, and if a program tries using a resource that is controlled by a faulty driver, the entire computer will crash easily.
Updating your drivers is a good idea when tracking down possible problems. While you're at it, you should make sure your programs and operating system are fully patched as many patches contain stability updates that resolve common crash problems.