What's the deal with Aspect Ratios? There are plenty of other people out there who have already described Aspect Ratios in a greater depth than what I can offer anyone browsing on my pages, but I like to think of them as a picture frame's dimensions. At a superficial level, it might seem it's just up to whatever you decide (and it very well is), but the following might help you make informed decisions on what you prefer or what contributes better to the story at hand.
Some Aspect Ratio examples (generalizations):
4:3 is your super old TV set that looks like a box.
16:9 is the new TV you just bought sitting in your living room.
2.40 are typically the epic cinematic wonders you see in theaters - big landscapes, explosions, etc...
For anyone interested, here's a reference I made to help me put crop marks on my HD footage without going to a calculator every time:
Aspect Ratio: 1.33 (a.k.a. 4:3) [SD Aspect Ratio]
Dimensions: 1920 x 1442, 1440 x 1082, 1280 x 962
Aspect Ratio: 1.66 [Super 16 Aspect Ratio]
Dimensions: 1920 x 1156, 1440 x 866, 1280 x 770
Aspect Ratio: 1.78 (a.k.a. 16:9) [HD Aspect Ratio]
Dimensions: 1920 x 1080, 1440 x 808, 1280 x 720
Aspect Ratio: 1.85 [35mm Aspect Ratio]
Dimensions: 1920 x 1036, 1440 x 778, 1280 x 690
Aspect Ratio: 2.35 [Super 35mm Aspect Ratio]
Dimensions: 1920 x 816, 1440 x 612, 1280 x 544
Aspect Ratio: 2.40 [Anamorphic Aspect Ratio]
Dimensions: 1920 x 800, 1440 x 600, 1280 x 532
It's an easy calculation if you're trying to figure out vertical dimensions (Y) for editing footage. Just take your horizontal resolution (X) and divide it by the aspect ratio (AR).
X / AR = Y
Example: 1920/1.85 = 1037.8 ~ 1036
(Always keep dimensions even numbers. I always try to round downward to the nearest even number so that I don't run into any problems with rendering a thin black line on the upper and lower parts of the image, depending on how other software handled the aspect ratio crop.)