Home equity loans generally come in two flavors: 1) Fixed or variable rate loans for a specific amount and a set term, and 2) variable rate lines of credit. They are attractive because they carry lower interest rates than other types of loans and credit cards and the interest is usually tax deductible.
Home equity lines of credit (HELOCs) are very popular because they can act as standby emergency funds that can be drawn down and repaid as you see fit. Most lenders charge an annual commitment fee on the unused portion of the line of credit, so it doesn't make sense to have a HELOC much larger than you need. As with all loans, terms can vary widely, so spend the time to read the loan documents and ask questions if anything confuses you.
Home equity loans use the equity in your home as collateral. Your equity is the difference between the fair market value (FMV) of your house (the price you can sell it for as determined by an appraiser) and the amount you owe on outstanding mortgages. For example, if your home's FMV is $250,000 and you owe $100,000 on your mortgage, you have $150,000 of equity in your house.
Home equity loans are available up to a certain percentage of your equity (80% is common). Before the subprime mortgage crisis surfaced in 2007, it was common for lenders to loan up to 100% of your equity value. In certain areas of the country where houses were appreciating quickly, mortgage companies were offering equity loans that exceeded the owner's equity. That's changed now.
With a fixed term, fixed amount loan, you make principal and interest payments exactly as you do with a regular mortgage loan. When the term is over, the loan is paid off and closed.
A HELOC, on the other hand, allows you to borrow and repay funds up to the credit line limit as you please. HELOCs normally carry a term of 5 years, at which time the outstanding principal comes due.
Home equity loans can be used for anything you want. The deductibility of the interest is related to the fact that your home is collateral for the loan--and not related to how you spend the money. There are limits imposed by the U.S. Internal Revenue Code regarding deductibility of mortgage interest on large loans, so check with your tax practitioner if your total mortgages are anywhere close to $1 million.
Many people use home equity loans to pay off their credit cards in order to reduce interest expense. This can be a good plan if the borrower then stays away from the credit cards. Too often, the empty credit cards are just too enticing to leave alone. In a year (or less), it's back to maxed out credit cards combined with a home equity loan.
Oh, yes. People living beyond their means in hot housing markets tend to finance their lifestyles by continually converting their home equity into cash via home equity loans. When the housing market takes a turn for the worse, as it did in most areas of the United States in 2006 and 2007, a homeowner can end up with mortgages (primary mortgage and equity loans) that exceed the fair market value of the home. This makes lenders nervous and can result in them demanding a payment to correct the "upside down" situation. Got cash?
Personal loans can be uncollateralized (often referred to as signature loans) and collateralized. Collateral for personal loans can be just about anything the lender is willing to accept, such as a car.
Interest on personal loans is not tax deductible. That makes them more expensive than home equity loans, not to mention that interest rates are also generally higher.
When you get right down to it, there's not much difference between the two. Credit cards are simply signature lines of credit (except for collateralized credit cards used by people trying to establish or re-establish good credit records). Most people don't buy automobiles using credit cards, preferring instead to take out an auto loan over 3 to 5 years. Interest rates are generally better for auto loans and quite frankly, not many people qualify for credit cards with $25,000 or $30,000 limits.
The prime rate is the baseline for determining personal loan interest rates. Your credit score weighs heavily in the calculation (see Credit Reports & Monitoring for a discussion of credit scoring) along with other factors, such as quality of the collateral, employment history, down payment amount, etc.
Shop around. Just like differences you see between grocery stores on their prices of milk, lenders vary on their interest rates, lengths of loan terms, etc. Get quotes from lenders before you apply for a loan. Applying for loans from several lenders can hurt your credit score, so it's best to make your decision regarding which lender to use by collecting information outside of the application process.

Credit card debt can swallow you up. If you have the discipline to stay away from them, a consolidation loan makes good sense.