My spouse and I have been following the Dave Ramsey plan for years. We are in "baby step" six, but we still technically have credit cards. We just pay them off 100% in full as soon as we put any charges on them. That way, we get the rewards, but don't have any "debt" and don't have to pay any interest.
Personally, I fell it comes down to knowing yourself and self discipline. The plan that Dave gives on the radio has to work for the entire audience. Most people (even though they think they are) are not at a point where they can responsibly use credit cards. Unless you treat them the same way Dave treats debt, in that you will never, under any circumstances use them to spend money that you don't have (even if you are in an "emergency") then you really are better off cutting them up.
There are also studies that show people spend more if they use a card (even a debit card) vs. cash, so there is that argument too. Personally, I'm letting convenience win on that one, even though the studies are probably right.
There are also people who use miles to justify larger purchases. "It's ok to spend a little more on this, because I'm going to get a free trip out of it." If you or your wife find yourself thinking along those lines, then it is probably best to cut them up as well, because then you really aren't mathematically coming out ahead.
In terms of cards, I use the Citi Double Cash card for pretty much everything I buy. It gives me 2% cash back on every single purchase. (No limits, no restrictions.) I never justify larger purchases with it, because 2% back on any amount is still 98% lost. Getting the 2% on everything I was already going to be buying anyway though adds up to a nice "bonus" each month.
I also cycle through signup bonus cards as well, whenever there is an offer to qualify for. If some company is going to give me $500 to put $3,000 on their card in three months, I'll switch everything to that card until I reach the amount, then switch back to my 'default' Double Cash card.
There also some cards that give 5% on specific categories (like gas or restaurants). I sometimes mix those in as well.
In terms of your credit score (someone mentioned it below) there are a lot of different factors that go into your score. Keeping your oldest cards open forever (as long as they don't have annual fees), and making sure you never miss a payment on anything you owe - are two of the best ways to keep your score up. https://www.creditkarma.com/ is a great site to better understand your credit score, if you are interested in that.
For sure. Justifying larger purchases has crossed my mind just to get the miles, probably a bad idea. So I will have to keep my wits about me and if that starts happening, just call it quits.
Seems like you have your financials in good order Tim, good on ya bud! If this one goes as well as I hope, maybe I'll dabble into the "bonus" card idea if one happens to appeal to me.
Thanks for your long and thought out response, I really appreciate it!