I have two old dumb phones in addition to my iPhone 5s.
One is an old Motorola flip phone, originally on the T-Mobile prepaid network. The other is an AT&T-branded Huawei candy bar phone, another prepaid phone.
Both are unlocked quad-band GSM phones, meaning I can easily take them abroad and pop in a local SIM for voice calls/SMS. One of the phones permanently lives in my car as a backup should anything happen to my iPhone.
Currently, both phones are equipped with Tru SIMs. At $0.15/min. for US voice calls, Tru SIM is a bit pricier than your typical $0.10/min. pay-as-you-go prepaid service, but you can take the SIM abroad and not pay roaming charges in probably 50+ countries. Plus, you get to keep the same phone number.
With Tru SIM, your account balance doesn't expire ever, as long as there is minimal account activity. For me, that means sending a text every month or so. Incoming texts are free (at least here in the US). Outgoing texts are something like $0.10 each, but I have no qualms registering these phones on Google Voice since I don't get dinged on forwarded SMS.
So that's it. Two backup phones that don't cost me more than $2-3 per year to maintain, plus the flexibility of having a cheap handset that'll function with most cellular networks on this planet. I wouldn't pay a monthly fee to maintain these phones' service (or see expired airtime vanish), but I'm willing to chuck in a couple of bucks annually.
When you travel, you really want a backup phone, in the same way that you might give a set of your house keys to a trusted friend/family member, and make photocopies of important documents (credit cards, passport, etc.).