I've done it on almost every one of my employment contracts (didn't do it on the last one because it was entirely reasonable). I'm fairly choosy about what I strike out, though. For example one contract I had stipulated that I should compensate the company for any losses they incur if they terminate my employment. This is clearly unreasonable and I struck it out. They complained and I offered to GTFO if they really thought that the clause was that important to them. It turns out it wasn't.

I admit that in the past I have always had the luxury of feeling like I could turn down a job if the terms weren't right. I've never had to, though. Having said that, I have witnessed people failing to join companies I've been at because they couldn't come to terms on the contract. It happens.

I work on contract now, rather than as an employee, so I have a lot more flexibility with the contract. I suspect it will have to be that way forever because I'm at the point in my life where I refuse to sign an inventions agreement.

One side point that I think is important to point out is if your employer tries to get you to sign something new after you are already on contract, they usually have absolutely no leverage. They can't threaten to fire you over it because that would be considered duress and contracts can't be signed under duress (where I lived, anyway).

Whenever I get handed new agreements to sign when I'm already under contract, I always ask for compensation. No compensation, no contract. Usually the documents disappear in a wink. One time they didn't and all I had to do was phone up the legal department and say, "HR has given me this thing to sign, but I don't want to. They seem to be implying that I won't have a job any more unless I sign it. Is that really the case? I have my employment contract here and this isn't in one of the termination clauses..." In less than 5 minutes I had an apology from HR (Ha ha! I should have framed it. I'll never get another one!)

Obviously I'm not a lawyer. This is not advice (legal or otherwise). Consult a lawyer if you find yourself in similar situations.