There was an interactive chart available here, but the site is not available anymore. I've converted the website to an image in order to be able to save it for future reference.

Suggested books outlined in red
A similar roadmap can be found on Wikipedia: Link. I might convert the roadmap to the new link when I've got some time to be able to add new books, should something be released in the future.
I personally am around novel 30, reading it in the order of release. It is very difficult to give you an answer on which books to read and which to skip as it's heavily dependant on what subject of the Horus Heresy interests you and what you consider essential knowledge. So, I'd heavily recommend you to check the synopsis on the books by yourself and consider if you think it's worth reading.
Some books that (IMHO) are essential to understand the Horus Heresy:
- Horus Rising (Get an idea of Horus and how he ticks)
- False Gods (The root of the Heresy and how Horus fell to Chaos)
- Galaxy in Flames (Isstvan Dropsite Massacre, essential to understand later references)
- The Flight of the Eisenstein (How the Imperium learnt of the Heresy and how they reacted)
- Fulgrim (How Fulgrim fell to Chaos)
- Legion: Secrets and lies (How Alpha Legion fell to Chaos and why they're considered loyal to the Imperium)
- Mechanicum (How and why some part of the Mechanicum fell to Chaos)
- A Thousand Sons: All is Dust (How Magnus was tricked into service by Chaos)
- The First Heretic (How Lorgar fell to Chaos)
- Prospero Burns (How the fate of the Thousand Sons was sealed)
- Deliverance Lost (Raptor Project of Corvus Corax and how the Alpha Legion made sure it didn't succeed)
- Unremembered Empire (Imperium Secundus and the base for the Codex Astartes)
- Vengeful Spirit: The Battle for Molech (How Horus got the favour of Chaos and become their tool)
- Eye of Terra - Aurelian: Novella about Aurelian, specially part two of it (The Pilgrim) describes how Lorgar Aurelian became the traitor Primarch.
- Path of Heaven: What the White Scars had to endure and how they could go to Terra despite the Ruinstorm. Also gives more information about the Human Webway project.
- Praetorian of Dorn: Terra is attacked by the Alpha Legion way ahead of Horus and how the Imperial Fists defend against it.
Alpharius dies in this book.
Can't yet give any more "required books" to understand the Heresy as I am not yet any further. I'll update as I keep reading.
Why I consider the other books not essential, I've left out the novels containing only short stories:
- Descent of Angels
- Story of Lion El'Johnson being reunited with his legion
- Interesting to understand the Lion but IMHO not essential to get the greater picture of the Horus Heresy
- Battle for the Abyss: My brother, my enemy
- Story of a gigantic ship that attacks Ultramar but is stopped by Ultramarines
- Interesting to know that the Mechanicum was involved in the Heresy very early but not essential to get the main storyline.
- Fallen Angels
- Continues the story of Descent of Angels
- Again interesting but not essential to get the important points during the Heresy
- Nemesis
- Officio Assassinorum operatives try to kill Horus why a Chaos assassin tries to kill the emperor.
- Has no effect on the story arc.
- The Outcast Dead
- How legionairies of the traitors flee from a prison on Terra but are killed by a Thunder Warrior
- No effect on the main story.
- Know No Fear: The battle of Calth
- Word Bearers attack the planet of Calth and lay ruin upon it and summon the Ruinstorm.
- Interesting to understand how the traitors fight and how the ruinstorm came to be. It's sufficient to know that the ruinstorm was created by the traitors to block the loyalists. It has some effect on the Ultramarines and basically is the source of Guilliman for the Codex Astartes but it's the fight for a single planet.
- Fear to Tread: The angel falls
- Horus trying to bring the Blood Angels to his side.
- Has some impact on the Blood Angels but not on the wider heresy.
- Angel Exterminatus: Flesh and iron
- Fulgrim tries to attain daemonhood by sacrificing Perturabo
- Interesting to get how Fulgrim became a Daemon Prince and how Perturabo ticks but not essential for the wider heresy.
- Betrayer
- The attack of the Word Bearers and World Eaters on Ultramar and the summon of the Ruinstorm (that failed in Know No Fear).
- It's sufficient to know that Roboute had no contact with the wider imperium and was not able to travel to the help of Terra, which is also explained in Unremembered Empire
- Vulkan Lives: Unto the Anvil
- How Vulkan survives (he's a perpetual) and is tortured by Konrad Cruze
- Interesting to know how Konrad ticks, how Vulkan survives but has no impact on the wider heresy.
- Scars: A Legion divided
- About the White Scars and how they found out what happened on Proserpo. There is an internal fight between loyalist and traitor White Scars legionnaires and why they've decided to join the loyalists. But it's no turn point in the whole heresy.
- The Damnation of Pythos: Thinning the veil
- Iron Hands, Raven Guard and Salamders land on a chaos infested planet and must try to survive.
- Interesting to see what happens to a planet that's been infested by Chaos but has no impact on the wider heresy.
- Deathfire: Into the Ruinstorm
- Salamanders bring back the corpse of the dead Vulkan to Nocturne for him to ressurect.
- Interesting to get more of how the Salamanders tick and what they're willing to give to bring back Vulkan to Nocturne but no impact on the wider Heresy.
- Pharos
- Fight over the planet Sotha, where the Pharos is located.
- Interesting to learn about the Night Lords way of war but has no impact on the greater story.
- At the end, there is a hint that Tyranids were waiting for something like that.