I'm a workshop junkie, and one thing that I've heard over and over is the idea of giving students choice and voice in their learning. For a unit on Shakespearean literature, for example, give them a "menu" at the beginning of the unit. All of the choices on the menu relate to the unit and the objectives you have for them. The "main dish" would be the main activity that everyone must complete. The "sides" might consist of 3-5 choices for activities from which each student would choose 2-3. These are also required activities, but the key component is the choice each student has. Then comes "dessert." Dessert is optional usually, so you could offer a dessert as a bonus activity that can't be completed until the main dish and veggies have been done. Another option is a Think-Tac-Toe board. On this, you create a board with 9 different activities for your unit. Each student chooses three of those with the only limitations being that the choices must make a tic-tac-toe in any direction on the board. If resources permit (and it has taken me several years of grant writing to achieve this but it is worth it!), have sets of a multitude of classroom novels that students can choose to read. I teach a unit on the Holocaust and the history of prejudice and intolerance, and students can choose from a list of sixteen novels that pertain to this theme. Two of the titles are mandatory reads that we do as a class, and in the literature circle format, throughout the year students choose a minimum of three (but often up to seven) titles to read. Choice and voice really seem to empower my students, and I have been sold on the idea.
I agree completely with the two answers above. If students read relevant literature, they are more motivated to read. I don't use textbooks a lot in my literature classes. I cover the staples, of course, but many of the selections have no bearing on my students'lives. I do a lot of scavenging - I peruse short story and poetry libraries to find selections that will use the same target skills (inferences, summarizing, etc.) but that cover topics that will interest the majority. Many times the reading level is actually higher than what the textbook alternative is, but they don't mind the extra challenge because they are reading what they like (or don't dislike as much - it's baby steps sometimes!). Tim O'Brien is a popular author whose novels many of my students read, so when I pulled out a short story by him, they literally couldn't wait to get their hands on it. Sometimes they have to read things they don't like because that's how the world works - but they do it because that's not the norm in my room.
True differentiation can also make a world of difference for some unmotivated students. Most of the unmotivated students that I've had personally have been either those who were at the top of the class (read:bored) who already knew a particular skill being taught thus saw no purpose in completing homework or caught on much more quickly, or students who were at the opposite end, those who needed a lot of remediation and reinforcement. With differentiated curriculum, each group would work at challenge-level. The upper end students would face something that they would actually learn from rather than rehash the same concept, and the struggling students would see mastery of the new content as an attainable goal rather than the carrot they will never reach.