So being new to photography, I'm a bit unsure what situations the high end lenses would make a difference. You said that at f/8 or f/11 that most lenses look about the same, but if you go further down the high end shines, especially since they can go down further. So what would the typical situations be where you'd use an f/1.4? And what situations would you use the f/8 and above?
Good questions.
I'd use ƒ/1.4 for one of two situations.
First, if available light is very low; f/1.4 is 2 stops faster than f/2.8, which is where even the best zoom lenses top out. This means the difference between an action-stopping shutter speed of 1/250s and a motion-blurring 1/60s. Alternatively, it means the difference between a (relatively) noisy ISO3200 and a clean ISO800.
Second, I'd use f/1.4 if I need a very shallow depth of field. For standard portraits, I wouldn't use f/1.4 (I need the whole face in focus, and thus would stick to f/4 to f/5.6 for most shots), but for a lot of candid portraiture and special effects, f/1.4 is very nice to have.
Also keep in mind that most lenses perform best when stopped down by at least one or two stops. So, that means that even if I am shooting at f/2.8 with my f/1.4 prime, I'm probably getting sharper images than most f/2.8 zooms can achieve when wide-open at the same aperture (there are exceptions...the Canon 70-200 f/2.8L IS II is reported to be very sharp wide-open, and I can confirm that the 70-200 f/4L IS is extremely sharp at f/4).
Put simply, there are LOTS of good reasons to buy the fastest glass you can. And "fast" generally equals "expensive"; all that glass costs money to make.
I'd use f/8 or higher for landscapes, where I want a large depth of focus. Keep in mind that diffraction sets in at or around about f/11 to f/16 (depending on the sensor), so you may actually see LESS sharpness as you get smaller and smaller apertures, but f/11 should be fine for most DSLRs.
Keep in mind that many kit lenses are only f/5.6 at the long end of their zoom range. Which means f/8 is only one stop down, meaning the lens may not be at it's sharpest, even at f/8 (remember, most lenses are best when stopped down between one and two stops). By contrast, that f/2.8 zoom you paid so much for is stopped down by 3 whole stops by the time you get to f/8, meaning it's in its optimal sharpness range.