Fork offset/rake, in conjunction with head tube angle, determines trail. Given a set fork offset, the steeper your head tube angle, the more "responsive" the steering will feel - ie, it will be easier to turn the front wheel. Given equal trail, you should be able to move from a bike with a really steep HT angle to a bike with a relatively shallow HT angle without much trouble. They won't feel exactly the same, but it won't be too big a deal - the trail is the largest determining factor.

A bike with more trail will be more stable at higher speeds, but feel sluggish at lower speeds - this is why those stayer bikes have "backwards" forks. Coversely, a bike with too little trail will be stable at slow speeds and handle like poo while going fast (again, compare a beach cruiser to a stayer bike).