Question: My instructions that came with my kit said that I should let the bottles sit for 3 days, then age in the fridge for 10 days. If I don't refrigerate, will I get bottle bombs?

Advice on forums and other places says to leave them in the bottle for two weeks or even upwards of a month, I doubt every brewer has enough fridge space to store 5+ gallons of beer for 1 or 2 months. So, I am inclined to think they won't blow, unless I bottle with too much unfermented sugar in them. 

Will leaving them out in room temp, cause them to pop?
Are there any other reasons for me to refrigerate my beer, aside from taste?

Answer: 
DO NOT put them in the fridge after three days. You'll want to store the newly bottled beer at around 70 degrees for a few weeks. Since you are bottle conditioning, the yeast will need time to carbonate the beer. If you put the beer in the fridge now, the yeast will drop out before it finishes eating the priming sugar, and **you'll have flat beer.**

With respect to bottle bombs, you just have to avoid too much fermentation in the bottle. You do this in two ways: 1) Make sure that fermentation is finished before bottling, by taking successive hydrometer readings and noting no change for a few days. This allows you to know, for sure, how many fermentables are in the bottle. 2) Make sure to calculate and measure your priming sugar accurately. This point is often missed. Beer making instructions usually assume a 5-gallon volume when specifying how much priming sugar to use. You will probably have to adjust this, since **typically the volume of beer you collect is not exactly 5 gallons.** Here is one calculator that can help with that: <http://www.tastybrew.com/calculators/priming.html>
I agree with DAX, have put bottled beer directly into the fridge. It takes about 3-4 weeks, but will carbonate. The carbonation may be finer (smaller bubbles) but is adequate. Don't think it really adds much just did it many years ago as an experiment, comparing to room temp carbonation from same batch