I genuinely cannot remember the last time I needed to produce ID that didn't involve travelling to another country, so I just don't carry any. I live in the UK; there is (as the US) no government ID card, as there is in many other European countries.

My wallet is quite small, I will say; I just have a rubber band around a couple of credit cards and potentially some folded banknotes, so I don't carry general "miscellany". I may be an outlier; if I'm going out to the shops or the gym or some such, I'll also leave my phone at home.