It takes about two hours of continuous running for my central air conditioning to cool the house down. Is this normal?

Depends on what the starting and ending temperatures were. It might take a couple of hours to lower the indoor temperature 10 degrees on a hot day. And the cooler you want it the longer it will take. That is, it would take longer to go from 70 degrees to 60 degrees than to go from 80 degrees to 70 degrees. That's because the greater the difference between outdoor and indoor temperature, the faster the heat flows in. It is counter-intuitive to most people that you don't want an air conditioner that can cool your house very rapidly. An oversized unit is not a good idea. The unit should be sized so that it can just keep your house comfortable--say, mid-70s--on the hotter days you can reasonably expect. On those hotter days, the unit may run almost continuously. The reason is that the A/C has a second function as important as, if not more important than, lowering temperature: removing humidity. An A/C that runs just a few minutes and shuts off will not have the opportunity to do that, and may allow moisture to condense on surfaces, along with requiring lower temperatures for comfort. The moving air and lowered humidity from a longer A/C cycle will make your house comfortable at a higher temperature, and that will be most energy efficient.

Hungry Guy, if your A/C can't get 65 overnight, then there is a problem, in my opinion. It's probably in need of service. I'm saying the normal sizing is for 75 or so inside when it's a sunny 95 or100 outside. I may be off on these numbers a little bit, it's been a while since I used the charts, and I was never a pro, but you can get the idea. An A/C contractor can size a unit for 65 even on that hot summer afternoon, but he probably wouldn't unless specially requested.

A lot of question. to ask first:

What is the outside temperature?

What is the outside humidity?

How long has your house been sitting, without air conditioning?

Is your house weatherproofed with proper insulation?

A house sitting in 100 degree temperature for a long period of time, without air conditioning, is going to take a long time to cool down.

Same principle applies to cold outside weather as hot outside weather.

Has your ac always done this? if not first chech out your outside unit. there are two copper lines going into your home. one is cold and thick and the other is hot and thin. if the thick one is not cold but your ac has been on for a long time this means you need to have someone to come service it. another thing is the thin copper line should not be too hot to the touch if it is your outside unit coil is dirty. if nothing is wrong with the out side unit. you should replace your thermostat. it is not that expensive they usually run like 25 dollars is not hard to change. the instructions will help. just don't let the wires touch each other.

I would say that it depends upon the central air conditioning system that you own. As another gentleman remarked, it also depends upon the range of temperatures with which you are observing. My uncle owns a company http://www.detailwiz.com/lasvegas which works with a lot of people asking that question (if you don't understand why, he tints their home windows so they can use less a/c). Anyway, I would probably look at each system as an individual before giving a direct and concrete answer.

It is possible your air conditioning unit is at fault. However, it is also possible that your house needs better insulation.
We have a room that takes longer to cool than any other room in the house, thanks to a giant window on one side. The light from it just ramps up the heat like crazy. We live in Las Vegas. We don't need the extra heat.
I bumped into a guy at work that owns this company: http://www.lvtint.com . We're getting him to tint the arched part at the top of our windows with a decorative, frosted effect. That's going to block a ton of light and UV but still let in the light.
Hope this helps.