As a Brit too, I usually tip at restaurants. But not as much for other things. The thing you've got to understand is, there's a culture difference between Britain and America. (And probably other countries too.) In America, they don't have minimum wage laws, thus tipping most things is considered the done thing. Amost as if it's compulsory.
Not just for restaurants, but for anything. If in a bar, and you order a round of drinks you're expected to give a $1 tip for every drink you order. So if you order four bottles of beer, you are expected to give a $4 tip. Even though all the barstaff has done is opened four bottles. This is not only not expected in Britain, the barstaff wouldn't know what you were trying to do if you gave them such a tip. For most things, except maybe the most fancy of restaurants, tipping is seen as optional in Britain.
In the US, somebody brings you a pizza, you tip. Somebody cuts your hair, you tip. Some guy helps you carry your luggage to your hotel room, you tip. In Britain, they'd gladly accept your tip if you did this, but it's not really as expected. It's seen more as optional. The US is a lot more of a tipping culture. So I think the idea was that Rachel's dad not leaving a tip at a restaurant was seen as something extremely rude. In Britain, it'd notice, but it'd hardly be the biggest deal. I believe, we were meant to feel sympathy for Ross.
Hurricane sums it up nicely. What bugs me is that for shitty service you are still expected to leave a tip in the USA albeit a smaller one. What kind of message does that send to the people serving you?
Also agree, Rachel´s dad was out of line, then again he was always a jerk anyway.