What documents need to be shredded?
When if comes to reviewing grants and publications, from an ethical perspective, my understanding is that you have three duties:


To not compromise the authors' priority in their investigation of their ideas and their ability to capitalize on investments in preliminary work.
To not compromise any intellectual property claims through premature release of information.
To not expose the authors to potential embarrassment due to the harsh and mocking comments scrawled all over the place in red pen.


If you personally are behaving ethically, then it really comes down to how much you trust your recycling waste stream.  Is there any likelihood of a student, colleague, or other malicious agent going through the bin and pulling out the information, either intentionally or just in a search for scrap paper?  Shredding is definitely safe, but a low-priority piece of information in a big communal recycling bin with a latch is also certainly exercising a reasonable standard of caution unless you have reason to believe that you or your institution are being targeted for industrial espionage (yes, it happens).

Honestly, though, in most cases the information just isn't important enough to worry about.  An incremental paper presenting the next step of a well-established program, a badly written manuscript on its way to a well-deserved reject, a grant proposal filled with "you should totally fund us to keep doing what we're doing"---these sorts of things just aren't of much interest to anybody except the authors and their close colleagues in any case, and are probably perfectly safe in the recycling bin.  It's not ideal, but it's also very low risk.

Beyond ethics, I believe that there are also sometimes legal requirements, particularly when it comes to being an external reviewed of grant applications for government agencies.  In that case, the best thing to do is to ask the program manager involved.