When we were fishing the Kenai in Alaska this summer if you got 20 feet of space you felt fortunate. Luckily, everybody was pretty cool about it when lines inevitably got tangled or someone hooked up (I've seen things get real ugly on the Salmon River in NY). My personal space definition varies when I'm out west. On well-known waters, especially in the summer, I'll expect crowds although nothing like combat fishing mentioned above, and either slip in the cracks for a bit or head elsewhere; again, most folks are pretty easy going and will try to spread out as much as the situation allows. On lesser-known water, or places where a bit of hiking puts some distance from the pull-offs, I usually don't see another person; if I do, I'll give them a couple hundred yards, often more. On little blue lines, I hope I don't see anyone.
Regards,
Scott