From what I have researched, it is possible to wire LED light strips into the mains for a house, but there are several things to consider.
First you cannot directly solder the LED strip into the mains, you will need a transformer (also called a driver), to reduce the voltage of the mains to 12V, which is typically what LED strips use.
Stemming from the first point, to actually have a neat solution, you now need to hide the transformer, behind some plaster in the wall, in a recess, behind a fish tank so on.
In my case, I plan to have the transformer hidden above the ceiling, as shown in the following diagram (the blue is the mains cable, the red box is the transformer, and the green is the LED lights, there will be a further drop ceiling int he form of polystyrene blocks, that well go on the ceiling, leaving a 10cm gap between the edge of the wall, so as to hide the LED strips but allow the ambience of them showing):
It is important to note, that transformers may run warm or get hot, depending ont he load. Keep them away from flammable materials and ensure they are ventilated well to keep them cool and running smoothly (and from burning your house down).
I have been told that the power requirement of the LEDs need to be calculated carefully. You need to know the power usage per meter of your LED strips, most daylight white strips use 14.4 Watts per meter (W/m) but they can vary widely (I have seen 4.8W/p, 7.2W/p, 9.6W/p and 14.4W/p) - they vary depending on brightness levels, number of LEDs per meter (usually 30 or 60), the colours the LED can output (either plain white or RGB) and so on. Check the energy use of the strip, and multiply that by the length that you need. So a 14.4W/m strip for a length of 20 meters will mean you need a transformer that can output 14.4x20 = 288W at a bare minimum.
There will be a slight loss of power the longer the strip is, hence someone suggested that I try to split the strip into 2 segments of 10 meters for better energy efficiency. The theory being that due to resistance in the cabling, and heat output, the strip will require more than 288W (and end up drawing perhaps 300W), but I could not find exact calculations for this. By splitting it into two segments of 10m, each segment needs 144W or thereabouts. The transformers will also be a lot quieter and run cooler.
Other important factors to take into account are the type of LEDS used and the colour of the lights. You can get plain white LED strips, They range from a warm white colour to a bright white. See the following picture from seesmartled.com.
The plain white are slightly cheaper than the colour changing RGB kind, which typically come with a remote, or an switch of some sort to allow the changing of colours.
Finally placements of the LEDs also needs some consiferation, they should in my opinion be placed so that they cannot be seen directly, but rather the light is reflected off a matt surface. Reflective surfaces do not work well, as the light looks really focused and spotty, see the example below, with the reflective floorboard (might have worked better with carpet or a more dull surface) versus the ambient light on the ceiling, which is a matt surface and diffuses the light much better.
EDIT: Thanks to gregmac for the following:
Most of the strips I've seen actually have a limit on the total current they can handle, and so only allow you to chain power for a few strips at a time. You'd need to run separate wires for each set of segments you need; whether you power them with one or multiple transformers is your call. There are different wiring requirements depending on the types of LEDs you're using (individually addressable or not; white vs RGB vs RGBW), so you'll need to figure some of that out before you start.