I think most employers will have a blanket "we own your IP" policy. But most of them will also make exceptions (and in writing) on a case-by-case basis once you prove you're a valuable employee. Because obviously you're not going to actually do anything on your own time if it's going to be your employer's property, whereas if you convince them that there's a potential for good PR with no real cost, they'll go for it. Once you've demonstrated that you're good at your job, and your side activities won't conflict with that.
"But most of them will also make exceptions (and in writing) on a case-by-case basis once you prove you're a valuable employee."
The way you've phrased that implies that policy is reasonable. It isn't. Why should anybody have to prove that he is a valuable employee before he gets freedom to do what he wants (on a case-by-base basis) in his free time?
I think companies don't want employees who stop thinking when they walk out the door, and if they just happen to have a key idea while in the shower, they don't want to be blackmailed later on.
