You are right, this is definitely a great way to supplement your studies. If you like this sort of study, here are some books that I recommend (and I own all of them, so consider these first-hand recommendations).
Logical Chess Move by Move - Great beginner's book
Winning Chess Brilliancies (Winning Chess Series) - Another great one for beginners. Its by Yasser Seirwan, who has a real gift for explaining the flow of a chess game.
Chess Master vs. Chess Amateur - This one is a bit dated but still very good.
Mammoth Book of the World's Greatest Chess Games - This is probably my favorite. Written by 3 very good chess players, covers a wide variety games from throughout chess history. Great balance of analysis and explanation. I hope they update this one soon.
Best Lessons of a Chess Coach - This book is interactive and is great for teaching the "whys" of certain moves.