I juggle a variety of cards to maximize the cash back - all of these have no annual fee:
- Chase Freedom and DiscoverIt for 5% back on their respective quarterly bonus categories
- Chase AARP for 3% back on gas and restaurants (you don't have to belong to AARP or even be of AARP age to get the card)
- American Express Blue Sky for their special offers
- Amazon Store for 5% back on Amazon
- Target Redcard for 5% back at Target
- Citibank Double Cash Back for 2% on anything else
(don't ask me why those bullet points are highlighted that funny way!)
The Freedom card usually has 5% on grocery stores one quarter - I buy enough gift cards during that quarter to cover the vast majority of my groceries for the year, so having a card that gives a special rate on groceries isn't worth it for me, but could for you if you spend more than $1500/yr in groceries (the max for the 5% Freedom quarterly category) - in that case, look at the AmEx Blue Cash which gives you 3% on groceries with no annual fee.
ETA: I don't carry a balance on credit cards - ever. So having this number of cards is not an issue for me (I actually have others too, for more specialized purposes). But if you struggle with credit card debt, I wouldn't recommend having this many cards in your wallet each day.