I always give 2 weeks. Never had the company determine it was best I not stay but I've seen it happen to others. Particularly if they were going to a competitor.
I have ZERO issues with the company stating "well, we appreciate it but we'd rather have it end right now/here" it makes sense from a "what's best for the company" perspective and because I've never seen someone's new company basically say you can't come to work for us early.
You wanted out, they wanted you in - typically works out ok. Unless it's a situation where you are part of a large training class like a call center or something. But I've never worked those jobs.
Layoffs - all I've seen have had people given ample warning and even up to 90 days to find another position within the company if they so choose.
