568B is the most commonly used standard in networking in an enterprise, at least what I have been around. That is what I have always used during installs and at my house.
568A is commonly used in telephone installations when using 8 conductor wire due to the alignment of blue pairs and orange pairs in line assignments, line 1 and line 2 respectively, which complies with USOC wiring scheme. The green and brown pairs due not match up natively to the pin assignments, so after that is doesn't comply.
If you wire 568B on one end and 568A on the other, you will create a crossover cable. The TX pair on one side is linked to the RX pair on the other side and vice versa.
In theory, you don't have to use any standard as long as the conductor color used in pin X is used on the same pin on the other side, i.e. you could use pin 1 = blue, pin 2 = green, pin 3 = orange, pin 4 = brown, pin 5 = blue/white, pin 6 = green/white, pin 7 = orange/white, pin 8 = brown/white as long as you wire it the same on the other end of the cable. I wouldn't do this, but it would work.
Continuity (cable mapping) throughout the whole cable really matters when you are running gigabit ethernet due to the fact that two pairs are used for TX and two pairs are used for RX. Fast ethernet only uses 1 pair for TX and 1 pair for RX, so the other pairs are not used, unless you are using PoE. So, I might suggest to invest in a RJ45 cable tester. It can be done with a multimeter or I have heard of people making their own. I cannot speak for these, but a quick search of DealExtreme shows some cable testers (http://www.dealextreme.com/products.dx/category.314) on the cheap. I have orderd from them before and it is legit, but it will take about two weeks to get it from China. If you want a reliable tester and toner/probe in one, I would suggest the Fluke Intellitone 200 (http://www.provantage.com/fluke-networks-mt-8200-60a~7FLUK07T.htm) Note: The 100 kit doesn't do cable mapping.
I forgot to add, when you are terminating cable try to keep as much of the shielding on as possible, i.e. don't strip back 3 inches or a foot when terminating to a patch panel. This will cause other cable to crosstalk with one another and higher attenuation. Only strip back as far back as you need to terminate it. Try to maintain your twists when terminating to a panel or jack too, if you can. Straightening all the pairs and terminating will again cause unneeded crosstalk and higher attenuation.
Do not bend the cable at sharp angles. It should be gradual. Like signal15 said, cross electrical lines perpendicular, if possible. Provide adequate support for your cable. Don't let the weight of a bundle put stress on the internal twists of its members. If you screw up the cable some how by cutting it too short or break the shielding and the pairs, don't try to couple it. Just trash it and start over. A properly installed cable with adequate support will last a very long time and provide adequate speeds versus one that was thrown up there and left to degradate.
I would strongly suggest buying reputable cable. Don't use cheap cable. In my opinion, not all network cable is created equal. I would suggest purchasing your own patch cords with a molded all-in-one boot and plug as they generally are better made than what majority of people can make themselves. Again, buy reputable patch cables.
Start with your longest run and work you way to your shortest. You don't want to get 3/4 on a long run after doing your shortest runs first and run out of cable in the box. Again, don't couple it. Start with a new box. One piece runs only.
Sorry for the book. I just see people all the time that throw cable up and wonder why they aren't getting the speeds they want later on down the line or experience network problems.
EDIT: Redacted potentially incorrect information. My apologies.