All these books mentioned are fine, but really they're reiterations of the same thing. They all follow a breakdown by functional group. Most American-authored books do. I learned Orgo this way and I did just fine, but I think there is a better way. Which brings me to
Organic Chemistry by Clayden et al.
This book is organized by mechanism type and not functional group. And so you have a chapter called "nucleophilic substitution at the carbonlyl carbon" and "electrophilic addition to alkenes". The virtue of this method is two-fold. First, it gets students thinking about mechanistic patterns rather than trying to memorize thousands of individual reactions. Second, it brings together a plethora of related reactions that in a functional-group based book, would seem unrelated. For example, conversion of alcohols to alkyl halides and epoxide opening reactions might be treated in two different chapters in the conventional format, when in reality, they are iterations of a substitution at saturated carbon. I think this approach gets kids thinking more in patterns and less in minutaie, which is the biggest obstacle people face when taking Orgo.
Now, I'll warn you that this book is quite comprehensive and might have more than you need for your particular class. But for those of you who really want to understand organic chemistry, this is THE book, IMHO.
If you're not so adventurous, of the traditional books, I think Organic Chemistry by Brown and Foote is very good. I used it as an undergrad and it served me well. It is clearly written, has lots of great illustrations and interesting sidenotes.
For those looking for a supplementary book, let me recommend a classic: The Art of Writing Reasonable Organic Reaction Mechanisms by Robert Grossman. This book was made for advanced undergrads trying to learn how to systematically approach mechanisms. It formalizes in one place all the rules for writing a reaction. This is in contrast to the haphazard way most of us learn it in class.
If any one wants to chat more about Orgo, feel free to PM me.