This advice is more pertinent to people who have already built some credit.
These are the cards I have.
1. American Express Gold Rewards
2. Chase Freedom Visa
3. Barclay Visa
4. Wells Fargo Debit
5. Brooks Brothers Store
6. Amazon Store
I use my Amex for everything that I can. The perks are the best there are for an average to above average consumer. It's easy to rack up points. Triple on airfare, double on gas and groceries, single on everything else. In addition, they have a lot of great online offers for points (5x for Apple, Target, Neimann Marcus, etc.). They have great travel, entertainment and retail offers exclusive to gold card members. They provide terrific insurance, fraud protection and the best customer service there is. Plus they do frequent specials for all Amex cards, like small business Saturday ($25 statement credit for shopping at a designated small business on SBS) and the gift chain (I got $140 in Amex gift cards, $20 to Starbucks, $54 statement credit, etc. all for doing my holiday shopping online). It's $175 a year after the first year, but the benefits are well worth it if you use the card enough. And you have to pay the balance at the end of each month. It keeps you in check.
Chase Freedom gets used for all my purchases that I can't use my Amex for. It's a cash back card that also gives you $200 back if you spend $500 in the first three months. No fee for owning.
The Barclay card is from a few years back when I was first establishing credit. I don't use it anymore outside of once a month just to keep the line active.
I don't use my debit card ever. It doesn't give me any benefits, so there's no reason to use it. I don't use cash for the same reason. I also try to pay all my bills with my Amex when I can, which includes pretty much everything outside of rent (I could do that too, but the cost outweighs the benefit).
The Brooks Brothers card gives you 4x points on Brooks Brothers purchases. When you get to 2000 points ($500), you get a $20 gift card. I shop there enough that getting 4% back on my purchases is a a huge plus.
The Amazon card was just another card I got early on that I don't really use much because I don't shop on Amazon much. But I use it for textbooks and medical tools.
So for a quick run down, one rewards card, one cash back card and your debit card. That's all you need. My credit score is around 750 right now. Haven't had problems getting approved for anything. I have never carried a balance over once on any of my cards. If you're carrying a balance over from month to month, you can't afford what you're spending.