...an unsecured (or personal) loans provider will base their decision on granting you a personal loan by using your personal credit history. This is verified by a credit check to determine your credit rating...

...An unsecured loan is a loan that is not backed by collateral. Also known as a signature loan or personal loan.

Unsecured loans are based solely upon the borrower's credit rating. As a result, they are often much more difficult to get than a secured loan, which also factors in the borrower's income... (www.wikipedia.org)

This is what it would be called in the UK. Obviously for personal customers only, for businesses it would be called a business loan. If you wanted to borrow money to buy a car, do up your house or simply go on holiday, you would ask for a personal loan which would generally be unsecured and not conditioned on any particular purchase.

The main product other than personal loans that banks offer are mortgages, which are for the purchase of a property and are secured on that property.

gen•er•al-pur•pose
adj.
Designed for or suitable to more than one use; broadly useful: a general-purpose loan
http://www.thefreedictionary.com/general-purpose

If you're planning a major expense such as home improvements or the purchase of an appliance or even a vacation or wedding, consider taking out a General Purpose Loan with convenient monthly repayments.
http://www.garantibank.com/loans/consumer_loans/general_purp...

PERSONAL LOAN SCHEME
PURPOSE
General Purpose Loan for Individuals viz. purchase of new consumer durable articles such as computers, televisions, refrigerators, air-conditioners, music systems, kitchen appliances, furniture, carpets etc.
Also for meeting customer specific needs like expenses on marriage, family functions, medical treatment, education, travel etc.
http://www.indorebank.org/source_psegment2.htm