Do NOT cancel old cards.
The higher your total credit line, the older your credit accounts, the higher your credit score is.
It's OK to apply for new cards if you get good offers, your credit score might be negatively affected in the short term, but it will recover in a couple of years.
However try not to apply for too may credit accounts when you need to apply for a new mortgage or refinance your current mortgage.
Other things that can affect your credit score:
Lower overall utilization (good)
On a particular credit account, lower than 50% if you can, and must stay under 90% utilization.
(good if keep utilization low)
Never go over
credit limit Certain cards (e.g. Amex) allow you to increase your credit limit online without pull your credit report, take advantage this to increase your overall credit line.
Ultimately, the higher your credit score, the cheaper it is for you to borrow money.
Even you are a disciplined consumer who pays off your credit cards every month, who knows?
Maybe sometime in the future you will need to borrow money.
money.stackexchange.com/users/858/grokus
Does it make any sense to open another account, just to get the cash back?
This depends on several things, primarily how much you spend on your card.
Work out the math.
If you spend $100 a month, then you would only be getting $1.00 a month back, which wouldn't be worth having the new card.
Also, if you are taking any penalties for being late, you're better off cutting the credit cards all together.
Interest (often at 15% or more) will quickly outpace any money you would be getting back.
Would it be smart to cancel the Visa if I do?
If you can use the new card everywhere, yes.
This prevents you from possible non-usage charges, the paperwork associated with the card, and possible card misuse.
money.stackexchange.com/users/312/C. Ross
One reason to have two credit cards that hasn't been mentioned yet is that you have a backup in case one card is lost/stolen.
This can be especially helpful in a pinch while you're away from home.
In your case, you might keep the new card as your "backup", store it separately from the primary card (i.e. so they don't both get lost at once), and maybe use it for
some nominal monthly bill (Netflix or something) to avoid inactivity fees.
FWIW, Discover might not be my first choice as a backup, Visa/MC are accepted at more places.
money.stackexchange.com/users/855/bstpierre
Don't open another credit card account just for cash back.
The Visa you currently have is all you need.
The only reason I can think of for opening another account is if some place you shop regularly doesn't accept Visa.
I have an American Express charge card because Costco doesn't take other credit cards.
Credit scores depend on more than just total credit.
Here's the Wikipedia entry on credit scores .
Your actual score may differ between TransUnion, Experian, and Equifax.
money.stackexchange.com/users/873/Scott Lawrence
Two or Three credit cards are a reasonable number (if you are responsible enough to pay them off every month*).
An extra card or two at home can work as a backup if your wallet is lost or stolen.
This amount will give you more options on closing the account if you have problems with the card issuer in the future, or if you find a much better deal, without hurting your credit score.
You might as well take the bonuses from an awards card, because everyone subsidizes the people who use them.
Just check the 5% category on the card and see if you already spend a significant amount of money there in your budget.
*If you can't pay it off monthly, you can't afford it, and you're paying more for everything in the long term to the issuer, along with the least responsible and the most responsible people.
money.stackexchange.com/users/931/SpecKK
I just got a mailer from Discover offering a new card, with 5% back on some items and 1% back on everything else. However, I already have a Visa which I have had for a few years.  Does it make any sense to open another account, just to get the cash back? Would it be smart to cancel the Visa if I do?
How many credit cards do I need? Should I open another just for the cash back feature?
money.stackexchange.com
<credit-card><credit-score>
money.stackexchange.com/questions/2553
money.stackexchange.com/users/952/samoz
If you can use the new card everywhere then it could be a good idea. Don't open another credit card just for cash back.  Whether you should get a credit card for cashback will depend on how much you use your card and, even then, the answer will be subjective. Some people think that one card is enough, whilst others believe that two or three credit cards is perfectly acceptable. In any case, it is generally not a good idea to cancel old credit cards.
The answer to this question will depend on how much you use your credit card. The answer as to whether or not you should get a card for cashback will be subjective. How many credit cards you need will be subjective, with some people believing one is enough and others believing that two or three is perfectly fine. It is not a good idea to cancel old cards.