Well, let's start this by saying that from a pilot's perspective, EVERY takeoff is an abort, and EVERY landing is a go around. Both are practiced every time you get near the sim, and indeed, some exercises are totally dedicated to them. Both are randomly injected by the sim instructors, so you never know....
Go arounds can be so early in the approach that the passengers don't notice them, to so late, that the aircraft actually touches down.
Aborts can happen any time from the start of the roll, until the aircraft reaches a pre-calculated speed that we call V1. Once that is reached you always go. They are NEVER done from 'full speed' or after nose gear lift off, no matter how many times it is claimed by passengers. A high speed abort is a very high energy undertaking, and will almost certainly result in the tyres deflating. For any abort above 100 knots, (which is normally 30 to 50 knots below V1) I would call out the fire crews, as the brakes will be so hot that they may/will catch fire.
During the abort there are no configuration changes (i.e. flaps stay where they are). Spoilers will automatically deploy, full (available) reverse thrust will be taken, and held until you don't want it any more (as opposed to 70 or so knots normally). The braking system automatically applies maximum pressure to the brakes, and then lets the anti skid system control it from there.
A high speed abort is spectacular, but the hardest abort to handle is with a combination of strong crosswind, wet runway, and, believe it or not, low speed.
Reasons for an abort? Lots. I've only ever had one high speed abort (for real) and that was in a 767 in which the nose gear steering failed, with the wheel offset, and a low speed after the FO lost all of his instrumentation. In the sim though, there will be engine issues of all types. Tyres regularly fail in the sim, but rarely in the aircraft. Basically though, below around 100 knots you stop for anything, and above that only for major issues.
Go arounds. Well, I would be surprised if a major airport (i.e. Sydney, Singapore) didn't see a number of go arounds every day, and lots on days when the weather is poor. They can be initiated by ATC, and that normally happens when they think that separation standards may be infringed. Note that it's a prediction, not that they have been infringed.....the go around normally ensures that they aren't. Places with crossing runways (like Sydney or Melbourne) could have you sent around because the aircraft on the crossing runway is simply too slow to obey his take off clearance (and that could also have him given an ATC instruction to stop as well). In Singapore, the most common issue that I've seen is people who are slow to vacate the runway. ATC expect you off at the first possible spot, and the aircraft behind will be spaced based on that. Miss the expected turnoff, and the following aircraft will likely be given an immediate order to go around. It happens.....probably every day.
From the coughpit though, go arounds can be initiated for all sorts of reasons. Simplistically though, it comes back to the pilot deciding that he's not happy with whatever is happening. It could be a mandated go around, like not having the appropriate visual cues at the end of an approach (the FO calls 'minima', and you have two possible answers 'landing' or 'go around, flaps'), or perhaps not being happy with whatever the conditions are doing to you (shear, gusty crosswinds). Aircraft issues too, will normally result in a go around, as it's much easier to sort out whatever is wrong in slow time.
Procedurally, all that happens in a go around is that an attitude of about 13 degrees is selected (in the 380 anyway), TOGA power is selected, and then the aircraft is cleaned up. The attitude is no different to what was used at take off, but the sudden change in attitude, combined with the large power change, makes people think we are indulging in aerobatics.
How often? Well, when I flew the 767, and did a fair bit of domestic flying, I figured that I did about one go around per year. During my last five years on the 747, I think we had 3 go arounds, one in London (crosswind out of limits), and 2 on the same flight in Melbourne as a nasty front came through (an empty ferry flight). Multiple go arounds aren't all that common, and we do try to avoid them...even if we have the fuel, it's unlikely that we'd try a third time. I've done more go arounds in Sydney than anywhere else.
Oh, and the cameras. I'd have to admit that I'm not a fan of them, especially in gusty, crosswind conditions. You end up with the situation we've had mentioned earlier in the thread, in which a passenger is convinced the pilots don't know what they are doing, because he can't see the runway. Approaching touchdown, the aircraft could have up to 20 degrees of drift...it won't be pointing anywhere near the runway...in a Boeing, that level of drift could actually be held all the way to touchdown, though it will be reduced to less than 5 degrees in an Airbus. On one approach I did a few years ago, my view of the runway was through the FO's window for most of the approach...there was that much drift. I doubt that a camera would have seen the runway at any point prior to touchdown.