There may be several reasons for the rejection, including:
1) No credit - if you have never taken out credit before, you will not have a high credit score.
2) Bad credit - if you missed several payments, your credit score may be too low.
3) Identity theft - all it takes is one credit card falling into the hands of someone that has stolen your identity and your credit can be badly ruined.
4) Bankruptcy - filing for bankruptcy ruins credit scores and can make it nearly impossible to find credit.
5) Too much debt - if you already owe several thousand to lenders already (whether or not it is in the form of credit cards or school loans, etc.) you may not qualify for credit.
6) Too many sources for debt - multiple credit cards and loans, no matter what the amount owed, can badly affect your credit.
But no matter what the reason, your credit score may simply be damaged to the point where lenders are unwilling to provide you with another source of debt from which they do not have the confidence you will repay.
If you are rejected, ask the company that has rejected you why. If it is due to a low credit score or some other information they have on file, it is very likely they will tell you so you can call the credit reporting agency and rectify the situation.
Credit card reporting companies, like Experian (UK's largest credit reporting agency) often offer free or cheap credit reporting for individuals that need to check their credit scores. These reports will tell you exactly what has happened as well as what you can do to fix it. Sometimes it can take years to recover from a poor credit score, but the effort is worth the reward as having bad credit can be significantly harmful on one's life.
Some people worry that they may be rejected due to a form of credit blacklisting. Rest assured that credit blacklisting, however, does not exist. Credit agencies and lenders want to give you money, because the more money they give you, the more they receive in interest. If you are rejected from a credit application, it is likely due to a low credit score that causes these agencies too much hesitancy and worry that you may not make the payments, resulting in a loss for them.
While it may be easy to blame a credit blacklist as the reason you are receiving rejections, most likely it is due to a past history of credit problems that is your responsibility to fix.