When should I refinance?

When the cost of refinancing (whether cash or equity) can be recovered prior to selling the home Or if the rates are sufficiently low so that the cost of refinancing can be covered in an interest rate that is lower than the rate you now have but higher than today's best rate.

When a second mortgage is a good idea?

To avoid PMI (first mortgage of 75%, and a second of 15%).

To diversify risk and get a low(er) LTV first mortgage. This is especially valuable when credit or income histories may not meet the rigorous demands of FNMA or FHLMC requirements.

When the borrower wants a fixed rate mortgage, but plans to pay off a significant portion of the loan within a specific time period. This allows the prepayment and a corresponding decrease in monthly payment. ARMs allow this prepayment with a corresponding drop in monthly payments, but fixed rate mortgages do not allow this advantage.