It's not real critical. When wiring phone centers we used metal raceways (or a thrown-together wood one) in the ceiling, but for my house I used pipe clamps like the one you posted at about 4' spacing. I like to add a wrap of double-sided velcro around bundles going to the same box, also about every 4'. Near the demarcation point I might use a few screw-in hooks like those used to hang bicycles if there are a lot of cables going out in one direction.
Don't fasten the cables to anything too securely. That way you can use the old cables to pull a new one if it becomes necessary.
One important detail: do not use zip ties. They can constrict over time and damage the cables they're wrapped around. (They're also tougher to pull new cables through than velcro loops.)
You didn't ask about routing them, but I guess it's relevant to explain the assumptions my recommendations are based on. I always do horizontal runs in the floor/ceiling and then run vertically within the bay where the junction box is located. (Rather than meandering through the wall as shown in one of pumpkin's photos.) This means less holes to drill and usually less resistance when pulling the cables. I also leave an empty bay (two studs) between mains and network cables, so I don't need to worry about securing the drops (recommended distance is at least 1' apart when running parallel to mains).
If you wanted to make pulling new cables even easier without doing a full PVC conduit setup, you can just install PVC fittings such as 90° elbows where the cables pass through the top plate or sole plate. That's were all the friction is going to come from when pulling, so some nice smooth PVC lining the holes can smooth things out nicely. (This of course assumes you'll use one of the existing cables to pull the new ones. Obviously you won't be able to run a fish tape without the sections of PVC connecting the fittings.) The fittings would also ensure that you don't go under the cable's minimum bend radius of 1 inch.
One other thing that I'll mention just in case is heat. Large, tightly-wrapped bundles of cable (think 50+ cables) that are being heavily utilized have the potential to trap heat in the center which can eventually degrade the insulation and cause shorts. Unless you're running a grid computing cluster at your house that's not likely to be a problem though. A more likely scenario for the average home owner is the use of Power over Ethernet, which will generate more heat. If you're planning to use PoE I'd limit bundles to 7 or 8 cables, just for good measure, even though I think the odds of a problem are still very low.
If your cables are running parallel to a power cable they will induce a small voltage on the line. The cable should have a ground wire at the entrance of the house this is usually bonded to a metal water pipe.
Verify that the cable ground is going to a well grounded place (metal Pipe or Conduit that is grounded). If you do not see a ground wire from the external cable box at the entrance to the house it was not installed properly, a ground needs to be added and that should eliminate your problem.
Best Answer
If you cross perpendicular to the power there will be no problems no matter how many cables you cross each cable basically cancels when perpendicular.