It would vary based on what the students can offer and what the organizations need. Perhaps you want to consider grouping your offerings into categories, e.g. Research (Surveys, Focus Group, Consumer Trials, etc), Design & Animation (logo, advertisements, etc), Event management, etc. The event management task can be pitched to various audience ranging from the corporate communication team, marketing team or even the HR team.
in terms of keeping the ball rolling, it would be mutually beneficial to sum up the working experience with some feedback/review. Not only does this help them to recollect their "good/bad" experience, it can help others to make their decision on engaging students. I personally think Email newsletter are not dead and are still vital communication piece where you can remind your audience of your presence and offerings. ;)
Agree with Sergio, there is a huge opportunity to extend it to a larger pool of students, and they do not necessarily need to be from harvard or stanford.
I was fortunate to be offered such work/project opportunities while i was in school. The ability to work on actual products and events make the learning so much more meaningful and realistic. The opportunities came from the lecturers' personal contacts, which means projects are few and sporadic.
In the previous organizations i worked with, I approached my ex-polytechnic for students to work on a medical e-book project. The lecturer swiftly gathered a team for us. We provided the content and the students would work on the graphics/animation and content layout. The output was great and at a fraction of the cost if i had used a design house or publisher.
For university students, we offered them to conduct a health awareness research. The students conducted the field surveys and shared their analysis (though the project was caned midway due to unforeseen circumstances).
You could possibly look at different type/level of tasks to match with the appropriate level of students. For example, a firm is looking to celebrate its 10th anniversary with a big celebrations. Students taking event management could be brought in to plan and run the event together with the firm, students taking public relations and communications can be roped in for PR and social media efforts.