AAC&U has published a very useful paper about that lists and describes some of these: First Year Experience; learning communities; experiential learning. At research universities like UT Austin, a lot of energy has been expended on encouraging faculty to find ways to involve undergraduate students, even first-year undergraduates, in their research. Research is a core part of what we faculty do; and it is an excellent way for undergraduate students to learn in a new way and to interact with faculty and graduate students outside of a classroom. There is increasing evidence that undergraduate students are more likely to persist in their degree programs if they get involved in research early in their training.
In the natural sciences, it is relatively easy to bring inexperienced undergraduates into the lab and find tasks for them to do. It is far more challenging to find tasks that engage them but also don't depend on expert skill. As anyone who has worked with students knows, it takes time and skill to find roles for variable levels of experience on a research (or teaching) team. It also takes a lot of patience. Still, it has become much more common for undergraduates to begin working in research labs in the natural sciences as well as the social sciences (e.g. psychology and sociology, where undergraduates can be very helpful in the collection of survey data, data entry, etc.).
Some disciplines, however, do not lend themselves very well to cooperative research with undergraduate students. This is true for literary studies, and especially for literary studies in foreign languages. Even as graduating seniors, students do not have the expertise that would allow them to perform even fairly basic research tasks. The sorts of tasks they could perform, like organizing a bibliography, are not likely to engage them. While the archaeologists in my department can develop interesting projects for inexperienced undergraduates, it is much more challenging for us literary scholars. I have tried to have students help me with a range of different parts of my research, but have never found a good project that was both useful to me and engaging for the students.
The place where I've found collaboration with undergraduates to be most satisfying is in my teaching. Over the past two years, I've worked with teams of undergraduates as graders. This has involved training them to grade by a rubric and then meetings to talk about each question. Over the semester, I have a fair amount of contact with the students. They get to see the field from a different perspective and, in the process, get a refresher on their Roman history while earning some money. This summer, I have an undergraduate helping me build my online Rome class. She has done a wide range of tasks for me, from working on the question banks to writing scripts for short concept videos to working on a module of her own. None of this work is "grunt" work--the liberal arts equivalent of washing test tubes; and, in nearly every case, it involves a lot of thought, research, and close collaboration with me as we talk about pedagogy, course design, and the specifics of my previous experience in teaching particular content.
It had never occurred to me that, for a humanities professor, one of the best places to involve undergraduates in our research is via our teaching. Specifically, it is by involving them in the creation of teaching materials, whether collecting images or making short videos on well-defined topics or designing an online module. Each of these activities requires in-depth knowledge of the content (and the particular issues it might raise) but also careful thought about the most effective ways to teach this content to someone else. As I discuss the projects with my undergraduate student in our twice/week meetings, research issues in Roman studies come up repeatedly. These activities are creative and engaging for the student, and extremely useful to me. More than that, they give this student valuable experience in what it means to be a practicing academic.
Update (7/1/2014) Peter Newbury (@polarisdotca) made the excellent point on Twitter that the other significant way that undergraduate students are getting involved in teaching is as peer mentors. He gave the example of an Astronomy 101 class at the University of Arizona. UT Austin, in our redesigned Intro Chemistry course, is also experimenting with models of peer mentors. Click here for an op-ed I wrote about the role of peer mentors in that course. In some cases, the mentors take the course for credit; in others (usually when their role involves grading), the peer mentors are paid. When a peer mentoring program is run well, it can be an excellent experience and way for undergraduates to deepen their understanding of concepts in courses they've taken and done well in.