The main advantages and cons have already been mentioned in other answers, and so I won't repeat them, but let me touch on a few other lesser advantages of credit cards.
Credit cards protect against theft
If someone steals your credit card from you it's a nuisance, but only a nuisance. Credit card companies won't charge you for fraudulent purchases made on your card. By contrast if someone steals cash from you you're out of luck, and even a stolen debit card or check book can often leave you liable for any purchases made by the person that stole from you.
Credit cards protect you against bad businesses
If a company charges you for an item or service and doesn't deliver on what they promised you have little options if you pay with cash. While there are technically always legal options to seek compensation, in practice it's not worth the effort or cost to try to seek legal action against a company if they didn't ship your 50 dollar video game to you as promised; it's just easier to write off the money as a loss.
However, with credit cards you have a simple option, just tell your credit card company that you were cheated and they will give you the money back! Effectively they will refuse to actually pay the company you made the purchase from if they believe you have a legitimate claim that the company did not deliver what they had promised you. It helps that credit card companies give you the benefit of the doubt on such claims; for low-cost items they often take your word that the company did not properly deliver on your agreement without asking for any significant proof. I've only used this feature twice in my life, but it's still nice to know you have options if someone tries to cheat you when you buy with a credit card!
Credit cards are convenient
Paying with cash is slower than credit and requires you to carry around cash, or worse coins (which I refuse to ever deal with nowadays). Credit cards are just a more convenient way to make a purchase in most cases. Sure, a debit card can duplicate most of this convenience, but even with debit cards you usually need to enter a pin where for small purchases you can just swipe a credit card and go.
Credit cards can help you to keep track of your expenses
If you regularly pay everything with a credit card then each month you get a nice report of everywhere you spent money, and most credit card companies will even give useful tools for visualizing how that money was spent. This can be useful for tracking how you're spending money, determining if you're spending too much or what the biggest expenditures are etc; making it easier to generate and follow a budget. Though admittedly debit cards offer similar features.
The net result is that a credit card, when used right, is a significant improvement over other forms of payment. It's fast and easy while helping you to develop positive credit and giving you added protection and cash back (or other rewards) on the purchases. I've made hundreds of dollars just by using my credit card to make payments and taking the cash back.
Should you get a credit card?
The short answer to your question is that if you trust yourself to reliably pay your credit card off in full every month, and not increase your spending because you have a credit card, you absolutely should have a credit card. It provides a multitude of advantages over other methods of paying, and no negatives if used wisely. I try to pay everything with my credit card, to the point I'm annoyed when I am ever forced to use another form of payment!
Having said that, if you don't use a credit card responsibly, including paying it off in full every month, it can be very costly to have, as the interest charges and assorted fees add up very quickly! Credit cards can also increase the temptation of buying something you don't really need, or can't really afford to purchase at the moment, due to how convenient they are and how easy it is to swipe a card without thinking about how much something actually costs. A shockingly large number of individuals struggle with using credit cards responsibly; I have many good friends who have told me they will never get a credit card again because they have seen that they can't use one responsiblly.
If you have any doubt about your ability to use a credit card responsibly I would suggest erring on the side of not having a card and not risking temptation, as the harm of misusing a credit card is far larger than the rewards for responsibly using one. However, if you're confident in your own financial responsibility and ability to pay your bill in full at the end of every month then I strongly encourage you to get one as soon as possible and start reaping the many advantages!