For the past couple of weeks my system hangs for about a minute or two at random times.
I generally have thunderbird running and the hangup occurs when I click on a link that brings up a browser.
At first I suspected firefox of being the culprit but I switched to rekonq and got the same results.
I also have Konsole, Knotes, and Dolphin running. (It hung for 55 seconds between the words "Dolphin" and "running" as I was typing this.
I've tried running top in Konsole and checking to see what's taking up all the cycles but I see nothing in top that suggests a memory or cpu hogging app.
Has anyone else experienced such a problem?

What part of the system is freezing exactly? Is it just the Plasma Desktop, or does the whole display freeze, keyboard + mouse become unresponsive, etc?

I've experienced the same issue, although I've always rebooted my laptop by removing the battery and inserting it again... Next time I'll wait more than just 20 seconds, to see if it starts working again.

If it does not unfreeze after the 20 seconds or so, please also check the hard disk use (as the system could be swapping) and the responsiveness of keyboard indicators.

Now I've tried to wait, unfortunately that didn't do it. One thing worth mentioning is that it has only frozen while the battery has been discharging. This freezing business has not been evident while my laptop's charger has been connected.

In your case, is this a hard hang (no indications of system activity) or a soft hang (parts of the system responding still).

It's a hard hang. The screen just freezes and all on-going animations or videos just freeze. The cursor won't move and pressing CTRL + ALT + F1 does nothing.

Okay, unfortunately this is likely a bug within the kernel or a driver it is utilising. These can be fairly difficult to resolve unfortunately.
As this issue only occurs on battery, it could very well be related to CPU / GPU scaling - try changing the configuration of the power governors to either use a very conservative "powersave" mode, or maximum "performance" mode, rather than the default dynamic.