I was cooking and I saw flames shoot up from under the oven element ... why might this be, and what can I do to prevent this? I wasn't too concerned because it wasn't the food that was on fire but rather just something under the element, and fortunately the stove is metal, so there shouldn't be a huge fire hazard ... correct?
It might be a grease-fire
Take a good look under the heating element - there might be some pooled drippings or other food-gunk. You might need to clean it or just replace the whole unit - as some of the electrical insulation might have burned-off.
Either way, I wouldn't use ANY of the burners on that stove again until you're SURE what caused it.
You should be worried anytime there's a fire you didn't intend to make.
Friendly safety reminder: You do have a working fire-extinguisher in your kitchen right? And your smoke-alarm has fresh batteries\is tested regularly?
Some electric ovens have an exposed electric element on the top which can be used as a grill (electric broiler). If you haven't cleaned your oven lately then you can get grease flaring up when the element gets very hot. Although most of the time this just makes some smoke these can turn into full-blown kitchen fires so I wouldn't ignore it. I'd suggest cleaning your oven with an over cleaning product, and then running your oven's self-cleaning cycle if it has one.