Spam is defined by Google as "Unsolicited 'junk' e-mail sent to large numbers of people to promote products or services. They key term in the definition is unsolicited. If you have agreed to join a mailing list and/or receive offers from a company (or their third parties) when you have entered a competition and they then email you - it is not spam!
We can't say for sure you won't receive spam by entering competitions, but too many people are quick to accuse companies of spamming despite having previously agreed to join their mailing lists or even in one Loquax case when we sent out a "You Have Won" email.
If you don't wish to receive emails from a competition promoter then you can (or should be able to) opt out of receiving emails when you enter a prize draw. Optting out should have no effect on your chances of winning.
If you're wary of receiving offers and competition related email then the best advice is set up a seperate email account specifically for competitions.