Total of 4 cards: two credit, two debit.
In 2007 my personal credit card was denied in Paris, France because spending money in Paris was considered "unusual activity" (?!), and in 2009 it was denied in Saudi Arabia for the same reason (despite the fact that I had informed the bank where I was going). At that time I only had a personal credit card.
That's why I now have two credit cards, one for personal, one for business use. They are both with the same institution and are linked to the same airline rewards program. I also carry two debit/ATM cards, one personal, one business, from the same bank....which is a different one from the credit cards.
I visit the ATM periodically to top up cash but never have more than $200. When abroad, I use the ATM cards to get foreign cash, and use my credit cards provided that there is no extra charge to do so. I did have my credit card scammed in Brazil in 1997, but newer cards have Chip technology so I am not worried about that.
I have not used travellers' cheques in the last 30 years. They are antiquated, you have already spent the money on the travellers' cheques before buying anything, and you can lose them too! I do as much banking online as it is possible to do. I never carry my chequebook with me unless I know I have no option but to use it.