My Dick Grayson Recommended Reading mostly takes place in the Post Crisis on Infinite Earths timeline. This is the version of Dick that I mostly prefer and treat as "canon," with a few exceptions. This list should give readers a good understanding of Dick's time as Robin, and a great understanding of his time as Nightwing and Batman. This list will be roughly laid out in order of events in Dick's life, rather than publishing order. For that reason, some books will be placed earlier than books they were published after. Most of these will also be available for purchase on Amazon, or through your local comic shop (support local business!).
Batgirl/Robin: Year One
This book serves as a great introduction to Robin in his earliest time with Bruce and Alfred, as well as his first meeting and flirtations with Barbara Gordon, a.k.a. Batgirl.
Teen Titans: Year One
This book is a cute introduction to the Teen Titans, the team of sidekicks who became heroes in their own right. This volume includes the "Fab Five" of original Titans: Robin, Wonder Girl, Speedy, Kid Flash, and Aqualad.
The New Teen Titans
This series, published from the early 80s to the early 90s (though going through several name changes) charts the reestablishment of the Teen Titans, introducing new members like Cyborg, Raven, and Dick Grayson's first love, Starfire. This series includes Dick Grayson's original (and in my opinion, superior) transition from Robin to Nightwing. It is essential reading up to and including The Judas Contract.
Nightwing by Chuck Dixon
Contained in 8 trade paperback volumes, Chuck Dixon's original run on Nightwing sets the standard for all modern Nightwing stories to follow. Released after Crisis on Infinite Earths, the relationship between Bruce and Dick is more tense than in the New Teen Titans, and serves as part of Nightwing's catalyst to move to his now famous hometown: Bludhaven. This series is also where Dick and Barbara Gordon became a couple, and is therefore very important to his history.
Nightwing by Peter Tomasi
Contained in one trade paperback, Peter Tomasi's Nightwing closes out the Nightwing solo series before Dick took on the mantle of Batman in 2009. The Nightwing book had some rough years between Dixon and Tomasi, but the series ends on its highest note, showing a Nightwing at his peak in terms of skill and confidence. It's bittersweet that such an excellent run had to end, but the further adventures of Dick Grayson continue in several Batman books.
Batman & Robin by Grant Morrison
Contained in 3 volumes, Grand Morrison's Batman & Robin charts the early adventures of the new Dynamic Duo: Dick Grayson (Batman) and Damian Wayne (Robin). Flipping the traditional script of a dark Batman and lighthearted Robin, this series shows Dick Grayson stepping up in the absence of Bruce Wayne to look after his son and Gotham City. This is the foundation for the Dick & Damian bond which continues to present day.
Batman: The Black Mirror
Only one volume, The Black Mirror is Scott Snyder's first work on Batman. It digs deep into the psychology of Dick Grayson as Batman, his relationship with Gotham, the history of the Gordons, and James Gordon Jr. Elements of this book carry over into the New 52, and it is an interesting character study of Dick Grayson, whose outlook on Gotham differs from Bruce Wayne.
The New 52: Nightwing by Kyle Higgins
Kyle Higgins' Nightwing is set after Flashpoint and the New 52 reboot. Therefore, all of Batman's (and therefore Dick's) history has been compressed into a much shorter time span. Due to this, certain things were cut from continuity (such as Dick's generation of Teen Titans). Despite this, Higgins is clearly a fan of classic Nightwing comics, and this series shines, despite the drawbacks of the New 52 era.
The Rebirth Era sees the return of Dick to the role of Nightwing after spending time as a spy in Grayson: Agent of Spyral. The first 5 volumes are written by Tim Seeley, who also wrote Grayson, so there are a lot of references. Vol. 3, "Nightwing Must Die" is my favorite of the first 5, as it also has a ton of callbacks to Morrison's Batman & Robin. Volume 6, "The Untouchable" by Sam Humphries is a great solo story which delves into the history of Bludhaven and one of Nightwing's oldest foes. Volume 7, "The Bleeding Edge" by Ben Percy, shows Nightwing going up against a new, high tech enemy. Unfortunately this story is not followed up on in Volume 8, as Percy left the book and Dick was given amnesia. However, the "Harm's Way" story contained at the end of Volume 7 is worth reading.