Because you mentioned some credit cards with high interest rates, I'll assume you're carrying balances right now. What happens next depends on your short-term financial goals and on your monthly budget.
If you're planning on buying a home or a car in the next two years, maximize your credit score while making some smart financial moves. Most credit scoring algorithms, like FICO and VantageScore, measure how well you manage your debt instead of your overall financial situation. Opening a new credit card may dent your credit score just enough that you could end up paying more in mortgage interest or car insurance rates than you'll save in finance charges.
Therefore, focus on trying to get each of your cards below 30 percent of their credit limits as fast as you can. Ask existing credit card issuers if they can lower your interest rate by restricting your high-APR credit cards from new charges. Unlike a balance transfer, you're not opening a new account that can ding your credit score. You're just reducing risk for your bank and enabling them to cut costs. Confirm that your lender will report your updated account as active to all three credit reporting bureaus before you sign the deal. (Many will.)
After your major purchase, or if you're just looking to preserve as much cash as possible over the short term, it's OK for you to take a hacksaw to your stack of credit cards. The latest credit-scoring systems still give you credit for the length of your oldest account, whether or not you keep it open. Find a balance-transfer offer that lets you consolidate as much of your debt as possible onto a zero introductory APR credit card. If you already have a good-to-excellent credit score, you should be able to find some solid deals from Chase, Capital One, Discover and other major lenders.
Then, cancel any cards with annual fees, so you're not tempted to rack up more debt. Finally, keep paying as much toward your balance-transfer deal as you did when you managed multiple minimum payments. Although your credit score will take a temporary dive, your on-time payments and positive credit utilization will eventually help you build a stronger credit history while you minimize fees and finance charges.