How much pressure should you apply when rolling on paint?
Don't stretch your paint.

The problem is probably not pressure (assuming that you remain consistent), but what I call "stretch". Folks tend to stretch the paint load of their roller or brush too far. With experience you'll learn what's the appropriate coverage area for a loaded roller. 

The goal, of course, is to end up with a uniform film of paint on the wall. If you're working your roller out past its range, you're forcing the dry roller through the film and creating voids in it. Instead, try this:


Load the roller with paint. My technique is to pull some paint from the pool up the slope of the pan, and then work the roller into it a few times so that I have even coverage all the way around the nap. 
Make contact with the wall 6-12 inches away from the newly-painted region. This drops the initial load of fresh paint on dry land, so to speak, and creates a temporary repository of paint. 
Work back to the previously painted zone, overlapping somewhat. Roll direction isn't important at this point. 
Work remaining excess paint from the repository outward, stopping when it becomes difficult to get coverage. This is the extent of coverage for that roller payload. Do not increase pressure to gain more coverage. 
Give the newly painted area one more roll, all in the same direction, blending with the previous area. Keep an eye out for voids and runs, which should be rare. At this point the roller should be fairly dry and not leaving edge lines. If it is, roll the edges out on new wall to clean them up, then re-roll the working area.


Using this technique I get consistently good results. For most interior wall situations, a coverage zone for a loaded roller is about 2ft. by 3ft. Maybe less. 

I also paint almost exclusively with quality 3/8" nap rollers. I don't mind a bit of stipple, which helps hide roller lines and wall imperfections. 

Or you have other problems.

All this said, if you're seeing streaks after a third coat, something else may be going on. Maybe you're rolling too long after the film starts drying. Maybe your roller has residual primer or paint of another color in it. Maybe the paint needs better mixing.