Spam is defined as unsollicited commercial communication and by now, everybody with an e-mail address knows what it means. It invades private and business mails, websites and can be relatively harmless or downright criminal. The European regulations of spam are severe, and the degree of severeness differs from country to country.

What can an on-line business send by e-mail without being considered a spammer?
If one wants to be on the safe side, one needs to apply the opt-in scheme. That means that any addressee needs to actively agree to receiving information from that specific commercial establishment beforehand. This can be done by ticking a box, writing an e-mail via a contact form etc.  Whenever a mail is sent, it must contain an opt-out option, e.g. "if you do not wish to receive this information any more, return this mail to xx@yyy.zz".
This is the law for all B2C relationships.

When dealing with businesses (B2B), the law is more lenient. It allows promotional mailings if a) the business addressee is already in business contact with the sender and b) the communication promotes similar products as the ones for which the business client was already in contact. WARNING: Austria and Germany apply opt-in also in a business context!

Spammers can "steal" a lawfully performing e-mail address and use it for their spamming purpose. This comes close to cybercrime as considerable damage to a business (reputation, unfair competition etc.)  can occur.

WIKIPEDIA article on Spam
and the very exhaustive German version
In Portugal: Comunicações publicitàrias não solicitadas

Related legal Wiki articles:
Cybercrime
Cybersquatting
Spam
Phishing
Spyware
Website privacy laws
CAN-SPAM act (US law)

Related Blogs and Fora:
How can we effectively defend ourselves against spam?
Spamming: Unter welchen Voraussetzungen ist die Zusendung von elektronischer Post zu Werbezwecken erlaubt? (Austria)
SPAM Laws in the U.S