Every time a user submits something through your website you should check for spam. You can be sure that as soon as your web site is on the web, spam robot will crawl trough it and submit every form they see.
Now, there are various ways to counter their attack. A very simple way is to add captcha to your form. But captcha aren't that effective and user tend to hate them. Another way is to let them submit, but then an administrator must approve their submission. Other site uses email to make sure user are authentic (forum registration for example). Other site blocks IPs that submit too many forms in x amount of time.
As you can see there is a lot of different techniques (and I haven't list them all). You need to choose the one that would work best for you.