Lecture notes, slides, homeworks, and exams from algorithms classes at UIUC and several other universities can be found on the web:
At UIUC:
Jeff's algorithms stuff: lecture notes, homeworks, and exams from 12 semesters of CS 473 and CS 573. Revised lecture notes will be posted on the schedule page throughout the semester.
Both Coursera and Udacity are offering complete algorithms courses, with videos, readings, and automatically graded exercises. By necessity, these courses tend to focus more on implementation and less on proofs and open-ended design than CS 473.
Algorithms: Design and Analysis taught by Tim Roughgarden, loosely based on algorithms classes at Stanford
For students who prefer an actual dead-tree reference, we recommend the following textbooks. The campus bookstore probably doesn't have them, but they're cheaper online anyway. I've asked Grainger Library to put copies of all these books on reserve.
Algorithms by Sanjoy Dasgupta, Christos Papadimitriou, and Umesh Vazirani (McGraw-Hill, 2006). Based on the undergraduate algorithms course at Berkeley. A complete draft of the book is available online. This is the closest traditionally published approximation to CS 473.
Algorithm Design by Jon Kleinberg and Éva Tardos (Addison-Wesley, 2005). Based on algorithms classes at Cornell. This is the standard recommended textbook for CS 573.
Introduction to Algorithms (3rd edition) by Thomas H. Cormen, Charles Leiserson, Ronald L. Rivest, and Clifford Stein (MIT Press/McGraw-Hill, 2009). Based on algorithms classes at MIT. The first and second editions are also fine. A significant fraction of this book has been transcribed into Wikipedia.
Algorithms (5th edition) by Robert Sedgewick and Kevin Wayne (Addison-Wesley, 2011). Based on algorithms classes at Princeton. This book doesn't cover everything in CS 473, but what it does cover it covers well; older editions are also fine. A crippled electronic version is available through the University library.
For review of prerequisite material, we strongly recommend the following online resources. (This stuff is also covered in several dead-tree textbooks, but really, why bother?)
Open Data Structures by Pat Morin, an open-content textbook (like open source, but for words) that really ought to be the standard reference for CS 225.
Other
We'll add more links here as we discover them. Suggestions welcome!