No, you don’t. A bad strapline is much worse than no strapline at all. It may be difficult to simplify what you do down into three or four words or you just may not have the kind of mind that can think up clever wording.
However, even if you don’t have a strapline it is good idea to try to construct a simple couple of sentences that can describe your business as you are sure to be asked for this time and time again.
I always suggest that rather than saying what you do, try saying what the problem is you solve, this is more useful and will make you stand out from the competition.
The most important thing is to be clear, not confusing.
If you do decide to have a strapline it is still a good idea to ask your designer to create logo files with and without the strapline so you can leave it out if it will be too small to be read.