Here are a few offers I would recommend not turning down:
1. Work an event for no pay. The idea of long hours doing menial tasks and going home with nothing but achy feet and empty pockets doesn't sound very appealing to most people, myself included. But working an event is an excellent opportunity to meet people you wouldn't get to meet as an attendee, plus it looks great on a resume. Make sure to do a good job and keep in touch with those people so you'll be fresh in their minds when a better opportunity comes up.
2. Take on a task you don't know how to do. We work in advertising. We're not doing brain surgery here. If someone asks you to do something you don't know how to do, Google it! If Google doesn't know how to do it, you're screwed. Kidding, kidding -- just ask someone for help. If you stick to the tasks outlined in your job description, you'll never get ahead.
3. Speak in public. Public speaking can be terrifying. I get that. But it can also be so good for your career. When you speak at a conference or event, people will come up and talk to you afterwards -- a far cry from networking events where everybody important is avoiding eye contact with people our age.
4. Write for free. If somebody asks you to write something that will be published, do it. Who cares if it's not paid? Be it your college paper, your friend's blog, or your company's newsletter, exposure is everything. Anything you can do to get your name out there will be beneficial to your career; plus, articles can be a nice addition to your portfolio.
5. Take unpaid freelance jobs. The economy sucks, and companies are looking for cheap marketing labor. If you're in school or unemployed, taking on a freelance project here and there could be really good for your career. It will sometimes pay or lead to pay eventually, but even if it doesn't, you should still consider doing it. It's an excellent opportunity to expand your network to new industries and meet new people. At the very least, you'll end up with something to add to your portfolio. If you're employed, freelancing might constitute a conflict of interest (especially if it's a paying gig), so check with your company first. If your company is okay with it, it's a great way to keep yourself inspired (and sane).
As entry-level talent in a crowded industry, we're not in a position to be demanding. Good jobs are few and far between, and only the most diverse, well-rounded resumes will get in the door. I say bite off as many opportunities as you can chew, and before you know it, you'll be a big fish.