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It is true that credit history and credit score are very important for survival. It is almost as if you are shunned by society if you have a dismal credit score. The bank wouldn't give you loans, the credit card companies will feel you are not credit worthy and wherever lenders feel you can be trusted, the loan comes with astronomical interest rates. Sure there are bad credit loans, bad credit mortgages and payday loans, but at the end of the day most of them are schemes to get you into further trouble than to get you out of it.
However, you can survive without a credit card and do well at that too. Unless you are in immediate need of lot of money to buy a house, property or a car, or you are totally debt ridden, you can still survive with no credit history at all and yet build a credit history for the future. You can start with opening an account. Interestingly, it is the bigger banks where you have a greater chance. Lenders look into your bank accounts, so it is always good to have one. However, you can still encash your checks without a bank account by going to the branch office of the bank where the account is held and get the money entitled to you by paying a nominal amount.
Agreed there are many places on the internet where you need a credit card to shop. In fact you even get some discounts for online shopping. You don't have to miss out on all the opportunities when you have the money, just because the credit card companies feel you have no credit history. You can buy a Visa prepaid card at Walmart. This refillable card can be used by you in every place where a visa credit card can be used. If you set the pin for the card, by calling the company, you can even use it as a debit card which solves most of your problems related to carrying around cash. You can do the same at gas stations. Interestingly, some of these gas stations and super markets report to the credit bureaus for the cards you take, which means you have started building a credit history. Another popular way is to open a PayPal account and get a PayPal debit card too which can be used like a normal card.