A simple answer would be a large reverberating NO.
If you're good at something, never do it for free. If you're starting out as a digital or graphic designer, or if you've been around for a few years, chances are you will be approached from time to time to provide free services in exchange for "exposure".
This generally means doing work that doesn't serve you or your interests, and more importantly doesn't expand your design knowledge or capabilities. Even when being paid, some of your work may be mundane or repetitive, but being paid for it and knowing that your skills are valued makes it worth while. But doing work like this for free doesn't benefit you or your industry.
Only take on PAID work. If you find things are quiet or you have some spare time, spend it experimenting on personal projects, expand on your current skill set OR better yet, enter design competitions on sites such as Zooppa or Talent House. At least this way your efforts may be compensated in cash rewards, or actual exposure with your name running alongside international brands and not a local trickster who claims to be an entrepreneur. Plus, even if you don't win, you have a great addition for your portfolio, this is unlikely to be the case if you produce free work of limited creativity for a "potential" client. I stress the word "potential" here as they are not your client until they are paying you.
You have a skill, you have a talent, you have no doubt spent years studying and struggling to get by to obtain the certificate to validate your gift, so now is the time to take it forward and do great work for people and companies that actually value it, to such a level that they will pay you for your efforts.
Would you ever dream of entering a garage and asking them to fix your car for free? Or would you pop into Ikea and ask for a new kitchen, based on the fact that you'll tell all of your friends and offer them exposure? You wouldn't do these things as they are simply ridiculous, this should be no different when it comes to creative services. The next time you are asked to provide free services, simply ask for their service for free in return, if they say yes then great, technically you've been paid, if not, then hopefully they have momentarily seen things from your perspective.
I recently had an enquiry from someone who wanted nearly £2,000 worth of video and graphics work completed, with an unrealistic deadline and wanted to pay less than 10% of the cost. Needless to say, I didn't take them up on their offer, as even working for a small amount isn't just slightly soul destroying but it's incredibly disrespectful.
Any client who wants a quality service will pay the necessary cost, they will hopefully see the value in your service and continue to work with you in the future. If not, at least you've been compensated for your time.
Unfortunately, design school didn't teach us anything about business, and we go into the post University/College world wide eyed and naive. Be proud of your profession, stay strong and most importantly, stay humble. Sticking to your guns about being paid isn't aggressive, it shows that you take yourself and your profession seriously, and ultimately sets you apart from the bumbling part time freelancer.
Work hard and be nice to people!