Yeah you can delete just a cell in a database. Some "purists" that insist on having their databases in what is called 6th Normal form (fully normalized) would say that is bad. But I am a strong believer that you VERY RARELY want a database fully normalized to the 6th level. A database should at least be normalized to 3rd normal form with possibility of going to 4th or maybe 5th if business requires it.
So in short, yes, you can delete just a cell by updating the row and setting the field to NULL (if the field is declared to accept nulls) or an empty string.
CODE
update mytable set myfield = NULL where id = 3
As for good or bad, I say it is fine as long as it is not a critical field (a key of some kind) and is considered an "optional information field". But don't let the purists scare you too much, a 3rd normal form table is just fine and even has its advantages over higher forms (like they produce shorter easier query statements typically).