The brand name is "BAND-AID" according to:
http://www.band-aid.com/index2.html

The brand name has one, but I think using it as a generic term, you can choose whether you use a hyphen or not.

1) Bob Geldorf's supergroup is correctly spelled Band Aid.
The brand of adhesive bandage is correctly spelled Band-Aid.
If used as a generic name for an adhesive bandage, there could be alternative spellings like band-aid or bandaid.


2) "Band Aid may refer to:
Band Aid (band), a musical ensemble raising money for famine relief
"Band Aid", a song on Pixie Lott's album Turn It Up
Band-Aid, a brand of adhesive bandage
A generic name for an adhesive bandage in America"
Source and further information:
http://en.wikipedia.org/wiki/Band_Aid

Further information:
http://en.wikipedia.org/wiki/Band-Aid
http://en.wikipedia.org/wiki/Band_Aid_(band%29


3) "band-aid
Alternative spellings
bandaid
Band-Aid

- Etymology
Trademark Band-Aid registered 1924 by Johnson & Johnson. Sense of a temporary solution 1968, Canada.

- Noun
band-aid (plural band-aids)
1. (capitalized, trademark) A particular brand of adhesive bandage.
2. (North American) An adhesive bandage, a small piece of fabric or plastic that may be stuck to the skin in order to temporarily cover a small wound.
3. (North American) A temporary or makeshift solution to a problem, created ad hoc (often used with a negative connotation of a lack of foresight)
1968, United Church Observer, n 15 (March), p 36:
It was another of those political band-aids patted over a minor sore."
Source and further information:
http://en.wiktionary.org/wiki/band-aid

Both are correct. If you are referring to the original brand then one would spell it as BAND-AID and if you are referring to a generic version of the product then one would spell it as band aid.