There are two primary reasons why I like to use credit cards and now have a decent number of them in my wallet (actually they don't all fit in my wallet anymore!). The first is the benefit of rewards (or statement credits that are effectively cash-back) earned via spending on the cards (as detailed on THIS LINK). The second reason is the potential to earn very lucrative sign-up bonuses when you first get the card. I'll highlight some of my favorite cards here ...
NOTE: This page is a bit out-of-date. I'm leaving it up because it still has some good info. But until I post something updated on this topic, please feel free to check with me before acting on anything on this page.
As always, I begin my discussion by referring you to my overall thoughts on "getting the best deal" and some credit card "warnings."
I'm going to keep this brief for now (might expand later on many of these cards). I encourage you to go to Miles to Memories, Frequent Miler, or Doctor of Credit to read more about many of these cards (and they are great resources in general on this topic and related topics). Specifically, both of these websites list most (or all) of these credit cards I'll mention (with lots more detail) under their "Hot Deals" tabs/links at the top of their websites. Both websites also have good discussions on how to think about how & when (and how many) & why to apply for multiple credit cards. Both websites also have links for applying to these credit cards (and the proprietors of those websites sometimes get bonus/credit if you sign up via their links - but what I particularly like about the Million Mile Secrets guy is that he vows to always tell us if there's a better deal available elsewhere than the deal available via his link).
So here's my list of favorite cards, with a brief description (I will try to add links to longer discussions about many of them at a later date) of why I like the cards - specifically whether it's for the ongoing rewards or the sign-up bonus (or both!) ...
A) Chase Southwest Airlines Visa. This is a great card for the value of the sign-up bonus, especially if you apply for TWO versions of the cards (one personal card and one business card) at the same time - in an attempt to win an unlimited-use companion pass for up to two full calendar years! Read about it in more detail HERE and HERE. Especially if you are able to get the companion pass, these cards can also be great for ongoing/daily use (as their 1.5% to 2% reward value for non-SWA purchases become effectively worth 2x that amount IF you earn the companion pass). Believe me, this is a bit of a complicated (or "advanced move") credit card "deal" ... but if you take the time to understand it, it can be VERY beneficial (if you do any amount of traveling at all). Our family flew to Washington DC a couple months ago "for free" (would have cost at least $2000 otherwise) purely from the benefit of signing up for two of these cards (and I still have quite a few miles left over!!). I could easily write a LOT more about this topic, but for now I'll suggest you follow the links above. This "deal" (getting 2 of these cards) comes around a few times per year (and arguably the October time frame is the best time to jump on the deal), but is currently only going to be available through June 29th (until it likely comes back again in a few months - so don't feel like you have to jump on it now!).
B) Capital One Venture Visa. This is a great everyday-use card, that I would highly recommend (either this or "C" below) for simply/easily earning 2% back on everything you purchase with the card. 2% is a lot better than the ~1% value that most rewards credit cards offer in terms of value (and a TON better than using a credit card or debit card that has no rewards!). The 2% comes back to you in the form of statement credits that you can use to "erase" any travel-related charges (at any point in the future), via Capital One giving you statement credits for the erased charges (making these rewards effectively as good as "cash" and completely flexible to use on any type of travel - rather than locking you into rewards from one particular airline or hotel). Capital One is currently offering a 40,000 miles bonus (worth $400 in statement credits) just for signing up for the card (as described HERE). The annual fee on the card is $59.
C) Barclay Arrival Plus MasterCard. I'll keep the description brief on this one, as it is very similar to "B" (above). The primary differences between the two cards is that this Barclay's card gives you 2% reward plus a 10% "kicker" (so effectively 2.2%) for spending, in the form of statement credits. While 2.2% is a bit better than 2%, the annual fee is a bit higher at $89.
Note regarding "B" & "C": Here is a LINK to a good comparison I found between these cards.
D) Costco AMEX (preferably the business version). This is a great card, as it is the only way you can pay with credit card at Costco (otherwise must pay with cash or debit) and you earn 1% back. But the best thing about the card is that you get 4% off gasoline purchases (at Costco or any gas stations) with the business version of this card, or 3% off for the personal version. You also get 2% back on restaurant and travel purchases, but you might as well use "B" or "C" to get 2% off. The only "downside" of this card is that your benefit comes in the form of an annual check that can only be used at Costco (but they will let you exchange your check for cash at the register - so you just need to restrain yourself from buying stuff you don't really need at Costco!). There is no annual fee on this card, as long as you maintain your annual Costco membership (for which there is a fee).
Okay, going to get REALLY brief in my descriptions for now ...
E) AMEX Blue Preferred Cash Card. Earn 6% back on groceries!!! (up to $6000 in grocery purchases per year)
F) AMEX SimplyCash BUSINESS Card. Earn 5% back at office supply stores (Staples & Office Depot), 5% on your wireless phone bill (if you're with one of the 4 major carriers), and 3% back on another "category" of your choosing (I chose Restaurants).
G) Target store credit card. Immediately takes 5% off all of your purchases in Target stores or their website, and gives you free shipping on everything from their website.
H) Chase Ink BUSINESS Card. Great sign-up bonus and earn 5% back on office supply stores, wireless phone bills, high-speed internet service, and TV service.
I) Chase Freedom Visa. A great card with ZERO annual fee. Decent sign-up bonus (for a no-fee card), but not great everyday rewards (1%). BUT the key is that they have a different quarterly bonus reward category that pays 5% back. For example, the category is restaurants this quarter, and during the 4Q (Christmas season) the categories include Amazon.com and department stores!