My car battery was dead recently, and all the taxi drivers I called to help me jump it refused to do so from their cars and would remove the battery claiming that it could damage their cars. They wouldn't even jump start it off their batteries while it was attached to their cars and would take it out to do so.
Their batteries were never powerful enough to get it going and if one of them had just done it with the engine running (reving a bit to give the extra power I needed) I wouldn't have had to go through so many taxis.
Thing is, I'm not convinced that they are wrong. I do think it's possible to harm the boosting car in certain rare conditions and haven't seen any of the advice advising you to start the boosting car rule it out. In this link
there's a bit about a guy claiming to explain why it can happen but I've heard an awful lot of mechanics claiming this recently using various reasons.
Anyway, my car in the states would turn off its lights automatically, and my car here in Costa Rica doesn't so I have had a lot of recent experience with jump starting and here are the things I learned when the jump start doesn't seem to work.
1) Sometimes you need to run the booster car for a while before the dead car will start and rev it a bit to get the other car going. I have seen this take as long as 10-15 minutes before the dead car will start.
2) If that takes too long or you don't want to wait you can take the battery out of the dead car, replace it with the battery from the live car and start the dead car. Then, while the engine is running you can swap the batteries again. Just don't turn off your car until you get home or are sure the battery itself isn't the problem or it might not start again (I also have a lot of recent experience with bad batteries because a lot of the "new' batteries sold here are refurbished old ones).
And a quick tip: get the positive and negative cables right, I've seen someone do it wrong and melt the cables in a shower of sparks.