Perhaps you rarely face it, but once you do, you surely know what's wrong: lack of free memory, or Out of Memory (OOM). The results are typical: you can no longer allocate more memory and the kernel kills a task (usually the current running one). Heavy swapping usually accompanies this situation, so both screen and disk activity reflect this.
At the bottom of this problem lie other questions: how much memory do you want to allocate? How much does the operating system (OS) allocate for you? The basic reason of OOM is simple: you've asked for more than the available virtual memory space. I say "virtual" because RAM isn't the only place counted as free memory; any swap areas apply.