I'll give you a UK perspective.
There was a time when there was a British - US divide in this. In Britain we used the self-effacing 'Don't mention it' and 'Not at all' for a smallish favour and 'My pleasure' for a larger one. 'You're welcome' was an exclusively US response.
But times have changed, the traditional phrases are falling out of use, and 'You're welcome' has have crossed the Atlantic to has taken over as the most popular response - doubtless as a result American media dominance. Along with it came many other more casual 'dismissive' responses such as 'No problem' (once an exclusively American expression), 'That's OK' and so on. There's even the Australian import 'No worries', which has become increasingly popular here, especially among younger men.
As for the 'Thank you' 'Thank you' exchange, that happens in shops, for example. The shop assistant thanks the customer for handing over the payment, the customer says thank you for handing over the goods, the shop assistant thanks the customer for their custom, while the customer says thank you for the service. So lots of thanking going on there! We're a polite nation.