Rate is locked
Most CDs from banks and credit unions are what's called fixed-rate CDs in which the rate will be guaranteed not to change for the entire term. This can be an advantage when interest rates are falling. I'm still earning over 6% on CDs that I opened a couple of years ago. However, this can be a problem when rates start going up.
Some CDs, especially those offered from brokerages, are callable CDs. For this type of CD, the bank has the right to terminate the CD after a call-protection period. For example, if someone opened a 5% 5-year callable CD last year with a 1-year call-protection period, that person will have to worry about that CD being called at or after the 1-year anniversary. Since rates have fallen considerably in the last year, there's a much higher chance of the CD being called.
Most CDs that you get directly from a bank or credit union are not callable. However, some banks have fine print that allows them to change the rate or accelerate the maturity. Two examples include NASA FCU (see post) and FNBO Direct (see post). The service reps from both of these institutions claimed that these features have never been used so the risk of losing your rate guarantee appears small for these cases.
Another way that you could lose your rate guarantee is if a bank fails. If the FDIC can't find a buyer for the failed bank, it'll mail you a check for the principal and accumulated interest up to the day of the bank failure. If a buyer is found (which is the most common case), the FDIC allows the buyer to change the CD rate. However, if they do change rates, they're required to allow you to redeem the CD without any penalties.
Penalty for early withdrawals
For regular CDs most banks allow you to withdraw accumulated interest from a CD without a penalty. However, withdrawing the principal will typically incur an early withdrawal penalty. Some banks will only charge you a penalty on the amount withdrawn. This is useful if you only need part of the principal. However, some banks do not allow partial withdrawal of the principal and will close the CD and charge you an early withdrawal penalty on the full amount of the principal. For these cases, it's a good idea to open multiple CDs.
There's a large range of early withdrawal penalties. The most common penalty is 3 months of interest for CD terms around one year and 6 months of interest on long-term CDs.
Some banks include in their disclosures a clause that allows them to refuse a request for an early withdrawal. As I described in this post there have been cases when banks have used this clause to refuse an early withdrawal request
Not everything in disclosures is bad for customers. Be sure to review the exceptions for early withdrawal penalties. In addition to the common exceptions like the death of the owner, some banks and credit unions allow customers over 59½ to make an early redemption of part or all of their IRA CDs without penalties. PenFed is one institution that has this exception (see post).
As I described above, when a bank fails and is taken over by a new bank, you can lose your rate guarantee. However, if that occurs, you are allowed a penalty-free early withdrawal. However, if the new bank decides to keep the rate and terms the same, you may not be allowed a penalty-free early withdrawal. This is what happened when WaMu failed and was taken over by Chase.
No additional deposits
Banks don't allow you to make additional deposits to regular CDs during the term. The only time you can make additional deposits would be when CDs mature. During the grace period at maturity, you can add to the CD. You can also make any other changes just as if you were opening a new CD.
If you want to add money to a CD, you have to open a new CD at the current rate. This gives you a hint at the advantage of a liquid CD that allows add-on deposits.
Liquid Certificates of Deposit
I'm currently working on a post to look into liquid CDs that lack one or more of the above features of standard CDs. I'll include reviews of all the nationally available liquid CDs. I already list many liquid CDs in my weekly CD rate summary.