Travelers' Cheques are outdated almost everywhere and with high fees.
If you're a couple, taking a Visa for one and a MasterCard for the other won't usually cost more than two of the same make and it's practical, as ATM fees can vary widely from bank to bank and city/country to city/country, depending on their favored card network there. Especially off the beaten track, i.e. in Central Asia, Africa, ... Remember also that in some countries ATMs are rare and/or decorative only, even in big cities.
In the Euro zone, if you have a European card in €, paying with a debit or credit card doesn't involve fees, and taking cash at an ATM or doing wire transfers is not more expensive than in your home country (usually, if you have a good bank, this equals 0 €).
Cash, in US dollars or Euros, is usually widely accepted or easy to change; if you're afraid of pickpockets (and rightly so in many places!), use a money belt under your clothes, it's very safe. Do not use money 'bags' around your neck – the necklace will be easy to cut for the robber. Cutting the belt and taking it while it's under your trousers/skirt/... is much more difficult!
In some countries like Uzbekistan wads of cash (and bags of cash) are usual because of the inflation and black market, but keep in mind that these are local banknotes, not hard currency! Do not show how much you have, or you'll be considered a 'dollar-on-feet'.
You may also keep small but sufficient 'emergency' banknotes in an 'international' currency like USD or EUR in a variety of places/pockets: don't put your all your eggs in the same basket.
Of course, all these things are less necessary in Europe or North America, where access to ATMs is frequent and varied, and where loads of cash (apart e.g. from Germany) are quite unusual!