Can I run CAT5/6 cables parallel to electrical cables?

You want to keep low voltage and high voltage separate so that stray nails, screws, and staples installed by less attentive individuals in the future can't puncture the cables and turn your low voltage wire into high voltage. There is always a chance some idiot is going to stick something electrically conductive where he ought not, and he probably shouldn't pay with his life for the mistake. (Nor should the home owner employing the idiot.) That's good to keep in mind even outside of construction/home improvement situations.

I have no idea what code actually says, but conduit is probably sufficient for the task, and shielded cable isn't. Distance would be the best option.

I think not a good idea, every power cable creates an electromagnetic field http://en.wikipedia.org/wiki/Electromagnetic_induction which will influence the other cables at least will lead to disturbances and errors.

As others have mentioned, there could be some interference. Most likely there is not a safety issue here if you are running parallel to standard plastic-sheathed NM / romex wire, but you may see reduced speeds. It's certainly not against code. You should at least use CAT 5e over CAT 5, as it is shielded better and can almost work at Gigabit speeds. CAT 6a would be your best bet, but probably a little overkill for you. When I built, I ran 5e in my house, and tried to keep it away from the the electrical as much as I could. There was some crossover and parallel runs, but it was kept at a min and I have been getting near gigabit speeds.

Note, manufactures have been using the term CAT6e, which does not appear to be a true spec. Seems like they are loosely using that as CAT6 with extra shielding. CAT6a on wikipedia.

Here is an article I found: differences between cat5 cat5e cat6 and cat6e cables

Be sure to use cables rated for in-wall Riser (CMR) use. That's a safety issue in the event of a fire. Use Plenum is rarely required in homes.

Its very simple; just don't put your Ethernet cables near any of power cables. Run your data cables 10" to 12" from your power cables. For future updates, put your cables inside conduit so that you can pull more cables or replace cables in the future.

I was told if the cable was rated at the same voltage as your power.you could even run them in the same pipe. Plus cat5 is twisted which also reduces electromagnetic interference. I actually had to put data and power in the same pipe for a fuel station

I'm not sure how much the separation needs to be. One thing I found says 24" unless things are shielded. If one or the other is shielded by metal conduit then you could use 12". If both are shielded 6". It was all alphabet soup. I could not find a official standard.

Data cables, coax, and low voltage in general should not run parallel to mains power. While people mention the need to avoid interference, the main thing to watch out for is induction. Interference will be annoying to equipment, but stray voltages will be destructive.

I had someone run coax along 120 AC in my house. It ruined a few cable boxes, a network router, and at least one motherboard. Once I moved the coax over a few feet these problems went away.

So two feet for parallel runs with any required crossings happening at 90 degrees is the rule I personally use.

Any cat cable that isn't S/FTP or F/FTP is going to cause problems if you simply want the outlets to be relatively close to the electrical ones (6" or so between the two), specially in the long run.

You don't want to go cheap with ethernet cables and this is important as there are good reasons for it.

Same thing goes with doors and windows of the house when you are buying or building a new one, or just want to change them as it's time for it after so many years... that's right, you don't go cheap.

I work in the cctv/security area. A bloke I work with ran the cat 5e utp next to a 3 phase cable for only 2-3 meyers(yes, I know) it fried the ipcamera. When I went to inspect, i touched the metal plug of the camera and it almost threw me off the ladder. I thought I connected it to 220vAC instead of 12dc. Don't do it. The whole thing apparently becomes a capacitor and it shocks like hell. Hope it helps!