Is it normal to see flames inside my self-cleaning oven? I spilled some sauce, cheese, and pepperoni in the oven last night while trying to transfer some homemade pizza from the pizza peel onto the pizza stone, so I decided to clean it today.

I wiped the bottom and glass door, but the rest of the stuff was crusty and stuck to the bottom of the oven.  I started the cycle and went about my business.

About 15 minutes later I hear a loud POP and I run over to find little flames dancing at the bottom of the oven.  I freak out, turn off the self-cleaning feature, grab the fire extinguisher and try to open the door, which wouldn't open (which I later found out was a safety feature because the temperature inside was close to 900 degrees, whew!)

Anyway, now my kitchen and living room are filled with light smoke that I'm trying to ventilate, and I am terrified to run the self-clean again for fear of my house bursting into flames unless I watch it (which I don't particularly want to, since the smoke is nasty).

So, were these little dancing flames and the resulting smoke safe and normal in the operation of the self-clean cycle?  If not, what can I do before running the cycle again to minimize flames and smoke?
Smoke is normal in an electric oven, but flames are definitely not.

In order to start a fire, you either need a spark, or you need to heat something beyond its autoignition temperature (AKA kindling point).  You might have had a short - or you might actually be using a gas oven with spark ignition - but I'm guessing your issue was the latter.

Cooking oil or grease being heated beyond its autoignition point is one of the most common causes of kitchen fires (grease fires).  Supposedly, some oils have autoignition points as low as 550° F (or 288° C), though I'm not sure which oils those are.  Olive oil would be my guess as the lowest, but pepperoni grease could very well have ignited at self-cleaning temperatures (which, as you noticed, go up to nearly 1000° F).

Fortunately for you, all modern ovens have a mechanical interlock which prevents them from being opened during a self-cleaning cycle.  If you'd opened it, you would have made the problem a lot worse by (a) supplying the fire with abundant oxygen, and (b) drawing all the hot air and flames out of the oven and into your kitchen, quite possibly setting your whole home on fire.  Heat wants to move to where it's cold; that's why you keep your doors and windows closed in the winter.

There are a multitude of oven cleaners available for self-cleaning ovens - you are supposed to use these before you run a self-cleaning cycle.  Yes, I know it's odd, but "self-cleaning" doesn't really actually mean that it cleans itself, it just gives you a little extra help.  You need to try to clear out all the grease and big chunks of food first using one of these cleaners, then run the self-cleaning cycle to deal with anything you might have missed.