Take a look at this screen shot from Pac-Man.

Specifically look up at the pink monster, you'll notice that its eyes (which indicate which direction it's moving) are angled down when it's not quite to the intersection yet. Now, take a closer look at the game boundaries.

The boundaries are rounded, which might just seem like an aesthetic choice on the part of the designers, but it's also a tool you can use. Taking a cue from the monsters you should try to press the direction you want to go before you get to the intersections. That way you can round the corner a fraction of a second faster than you would if you waited until you were in the middle of the intersection.

And in those higher levels, a fraction of a second can mean the difference between clearing the maze and putting in another quarter to start over from the beginning.