Every institution is different, but I'm generally of the opinion that from the minute your leave your house to the minute you get back you are on the clock, and everything "counts". (Assuming you're not also taking personal travel during the business trip, but that's an entirely different post).
There are some things that will almost always be reimbursed - taxis, busses, trains, airplanes, rental cars, hotels, conference registration. Some things are usually reimbursed - internet usage, business-related telephone calls, meals. Some things are usually not reimbursed - purchasing toiletries, souvenirs, entertainment, etc.
Sometimes something you think might not be reimbursed is, like room service or dry cleaning, and sometimes something you think will be reimbursed won't (e.g., upgrading from a $45/day car rental to a $46/day car rental of a larger size. I really wish I was joking on this one.)
Some US-based institutions grant employees "per diem" for non-lodging related expenses. This is a fixed sum based on location, and is meant to include food and "incidentals". It is given as a lump sum to the employee, pro-rated for the entire trip. If you're able to eat cheaply, you often end up making money on your business trips instead of just breaking even, which is pretty nice.
Other institutions want you to save all of your receipts, and itemize every expense. If you go out to dinner at a conference with 34 people it can get a bit tricky, some people get around this by asking for separate checks or getting multiple copies of the big check circling what they had. One colleague takes photographs with their phone to save time, which I think is pretty clever.
In any case, it's always worth saving all receipts and trying for reimbursement. There's no reason to be shy, or sweat over an expense you're not sure is reimbursable. Usually the worse that will happen is you'll be told "no".
Oh, one more thing. When you're on business travel, don't feel like you are required to share a room, stay in a roach-infested motel, or sleep on someone's couch. By the same token, don't stay at the Westin when there's a perfectly decent modestly priced place across the street. Be reasonable, and the people paying for your trip hopefully will be too.