Do I still have to pay penalties and taxes on money that I don't roll over from a DROP fund?

It depends.

Let's address the two penalties that will apply - the 10% early-withdrawal penalty and the 20% federal withholding - separately.

Early-withdrawal penalty
If the distribution from your Deferred Retirement Option Program (DROP) fund is made to you after you separate from service with your employer, and the separation occurred during or after the calendar year in which you reached age 55, then the amount will not be subject to the 10% early-withdrawal penalty, unless you qualify for another exception. (See list of exceptions below.)

Unless you qualify for an exception, the 10% penalty will apply if you separate from service before the year you reach age 55 and/or if the distribution occurs before you reach age 59.5.

If only a portion is rolled over to an IRA or other eligible retirement plan, only the portion that you keep (i.e. the amount not rolled over) is subject to the early-withdrawal penalty.

Federal withholding
Unless the distribution is processed as a direct rollover to an IRA or other eligible retirement plan, your employer must withhold 20% of the amount for federal tax purposes.

If only a portion is processed as a direct rollover, only the amount paid to you is subject to the 20% mandatory withholding.

If the amount is paid to you and you choose to roll over a portion to an eligible retirement plan, the portion that you keep (i.e. the amount not rolled over) is subject to income tax.

If your employer pays the distribution to you and you later decide to roll over the distribution to an eligible retirement plan, you may either:

-roll over only the amount you received (the gross distribution minus the withholding tax), OR
-roll over the gross distribution amount. To do so, you will need to make up the difference (the amount withheld for tax by your employer) out of your regular savings.

Exceptions to the 10% early-distribution penalty
The 10% early-distribution penalty will not apply if distributions made before age 59.5 are made in any of the following circumstances:

-Made to a beneficiary on or after the death of the employee.
-Made due to the employee having a qualifying disability.
-Made as part of a series of substantially equal periodic payments beginning after separation from service and made at least annually for the life or life expectancy of the employee or the joint lives or life expectancies of the employee and his or her designated beneficiary. (The payments under this exception - except in the case of death or disability - must continue for at least five years or until the employee reaches age 59.5, whichever is the longer period.)
-Made to an employee after separation from service if the separation occurred during or after the calendar year in which the employee reached age 55.
-Made to an alternate payee under a qualified domestic relations order (QDRO).
-Made to an employee for medical care up to the amount allowable as a medical expense deduction (determined without regard to whether the employee itemizes deductions).
-Timely made to reduce excess contributions under a 401k plan.

(For related reading, see Avoiding IRS Penalties On Your IRA Assets.)

This question was answered by Denise Appleby.