It Depends.
Do I let exceptions bubble up? Absolutely. But I want this for connection failure, command failures. Whatever you do, don't just hide these, you need to know about them. I prefer my applications to fail as quickly as possible to reduce side-effects and further damage.
I also log exceptions. I use Log4net to help with this. But I like to log exceptions at the source. I will let them bubble up from there.
Return null? If something cannot be found (i.e. looking for something by id and it isn't there), then I return null, not an exception. But there are cases where I could see throwing a new exception when this happens.
Main point: exceptions should be 'exceptional', not the rule. If an exception is thrown, it should be because something is really wrong and you need to fix it.