Detecting change in event properties

I have a table of (timed) events, and I'm interested in marking events
whose properties have changed from the previous event.

I believe this can be done with window functions, but I'm not sure
how. What window function can give me a field from the _previous_
row?

(To elaborate, I'm interested in:
* Finding field x of the _previous_ row
* Finding field x of the _next_ row
* Finding field x of the _previous_ row that meets a certain criteria
(which the current row may or may not meet)
)

I must say that window functions are amazing - they're a whole new
world, really.