Unexpected Extra Travel Costs and Grants When traveling, there are many things that can possibly happen or go wrong that would require extra money to fix.  While these things may not be directly related to the research travel one is doing, these expenses would not pop up if you weren't traveling. 

For example, if one gets stuck in the airport on the way back to one's home institution, you may need to get an extra night at a hotel before you go home.

The question is the following: When is it appropriate to claim such an expense on one's grant?

There are clearly varying levels of such events. One is something out of your control like weather pushing your flight back a day. Some are completely in your control and you messed up, e.g.,  you miss your flight and need to pay a fee to get on a later flight. Others are due to scheduling conflicts and new plans arising, e.g., another talking engagement shows up and one needs to pay the flight change fee in order to make sure one can present at both conferences.

Are all/some of these scenarios appropriate for claiming against a grant or asking reimbursement for?
These things happen, and as long as the expenses are reasonable, they should be covered by any reasonable funding body. It is a good idea to make a phone call to see whether you are permitted to spend the money, or at least to find out what budget limitations you have.

For instance, the other day my plane was diverted to a different airport. The only way I could make the PhD defence on time was using a taxi. So I took the 80 km trip and paid the 230 euro and fully expect that I'll get this money back. 

If I had have purchased a used car to get me to the defence and a bottle of whisky for pain and suffering, I wouldn't expect to get that money back.