From time.com

Who died by the hand of Thanos or his henchmen:

Loki: Loki offers fake fealty to Thanos and then immediately tries to assassinate the evil alien. Thanos doesn’t buy Loki’s trick and quickly murders him. Thanos quips, “No resurrections this time” after killing him.

Heimdall: Thanos and his children murder Thor’s best friend Heimdall (Idris Elba) when they invade Thor’s ship. But before he dies, the Asgardian opens up a gateway to Earth for the Hulk to escape.

Gamora: Red Skull tells Thanos that he will have to sacrifice something he loves in order to get the Soul Stone. Thanos apparently loves Gamora — just enough to throw her over a cliff. Gamora dies and Thanos walks away with another Infinity Stone.

Vision: Scarlet Witch (Elizabeth Olsen) destroys the Infinity Stone inside Vision’s (Paul Bettany) head to keep it from Thanos. But Thanos uses the Time Stone to turn back time and restore the stone and Vision. He then crushes Vision’s head in his hands and takes the Infinity Stone. Vision is left lifeless on the ground.

_{Note: Shuri might be able to fix him as she was working on something.}

Disintegrated by the Gauntlet effect:

Black Panther/T’Challa: Okoye (Danai Gurira) cries out as her king disintegrates.

Spider-Man/Peter Parker: Spider-Man disintegrated on Titan.

Doctor Strange/Stephen Strange: Doctor Strange disintegrates also on Titan. As he dies, he tells Iron Man that giving up the Time Stone to Thanos in exchange for Iron Man’s life was the “only way.”

Winter Soldier/Bucky Barnes and Falcon/Sam Wilson: Both got disintegrated in Wakanda.

Scarlet Witch/Wanda Maximoff: Like many others, she also got disintegrated in Wakanda.

The Guardians of the Galaxy Members: Star-Lord, Groot, Drax and Mantis — all four perish in the culling. However, director James Gunn has already confirmed that Guardians of the Galaxy Vol. 3 will happen. So some combination of these characters certainly be resurrected.

Nick Fury and Maria Hill: The former S.H.I.E.L.D. agents disintegrate in New York in a post-credit scene from the film — but not before they call on Captain Marvel for help.

Sure survivors:

Captain America/Steve Rogers: When he faces down Thanos one-on-one, Thanos inexplicably decides to toss Cap aside instead of just killing him.

Iron Man/Tony Stark: Despite being stabbed in the stomach, Iron Man survives. Doctor Strange trades the Time Stone to save Iron Man’s life.

Thor: With the help of his new battle axe, Thor is able to stab Thanos in the heart. Thor survives, but he doesn’t stop Thanos from destroying half the universe.

Black Widow/Natasha Romanoff: Black Widow takes out several of Thanos’ children in the battle in Wakanda and survives the fight.

Hulk/Bruce Banner: Bruce Banner also manages to live despite his inability to turn into the Hulk for most of the movie.

War Machine/James Rhodes: Rhodey lost the use of his legs at the end of Captain America: Civil War (though he can now walk with the aid of Stark technology). At least he made it through the end of Infinity War.

Rocket and Nebula: Of the original Guardians crew, only Rocket survives. Gamora’s sister Nebula also lives.

Okoye and M’Baku: Black Panther may be dead, but Wakanda lives on. Okoye and M’Baku survive.

Went M.I.A.:

Shuri: Black Panther’s sister Shuri tries to remove the Infinity Stone from Vision’s head, but is thrown from her lab by one of Thanos’ children before she can finish. We don’t see what happens to her when half the world’s population disappears.

Pepper Potts: The last we heard from Pepper, she was berating Tony for abandoning her to fight evil — again. We don’t know whether she survived the culling.

Captain Marvel/Carol Danvers: Nick Fury called Captain Marvel right before he disintegrated. The new, extremely powerful hero probably survived the culling and will likely swoop in to help save the day in Avengers 4.

Hawkeye/Clint Barton: The archer (Jeremy Renner) was conspicuously missing from Avengers: Infinity War. He was on some house arrest.

Ant-Man/Scott Lang: We know from the Ant-Man and the Wasp that Ant-Man (Paul Rudd) was put under house arrest after the events of Captain America: Civil War and before Infinity War. Scott Lang (Ant-Man) survives the event, but appears trapped in the quantum realm.

The Collector: We see the Collector (Benicio del Toro) alive and well in Thanos’ alternate reality, but then discover he’s not actually hanging out in his museum. Did Thanos kill him? Did he flee? Did he survive the culling? We don’t know.

Wong: Wong (Benedict Wong) returns to the Sanctum Sanctorum to protect the building after Doctor Strange is taken captive by Thanos’ children. We never see whether he lives or dies.

Other survivors who did not appear/are not mentioned in the film itself:

Valkyrie: She also survived somehow with a few other Asgardian/Thor 3 survivors (and maybe Korg and Meek too). Refer to this question for more details:

Where was Valkyrie?

Other major characters:

We don't know the status of Eitri and Red Skull/Stonekeeper. Red Skull should be free now as he doesn't have to be a stone keeper, but we don't know if he got disintegrated or not. Most probably Eitri survived as the Gauntlet is burned up and they might need him in the sequel to make a new one, as per speculations/assumptions.

Black Order Members (Corvus Glaive (stabbed for now but he can come back if he is depicted same as comics counterpart), Proxima Midnight (crushed by a giant machine), Ebony Maw (died in outer space when forced out of the ship through a hole), and Cull Obsidian (exploded in air by Hulkbuster (Bruce)).

Since you're asking for our heroes who died at the hands of Thanos and his henchmen, here it is.

Looking into the details given at this article, here are the casualties.

1. Loki: He was killed when he tried to fool Thanos for Tessaract.

2. Heimdall: He was killed by Thanos and his henchmen. He was half-dead after attack by Thanos' Black Order, and later stabbed.

3. Gamora: In order to get Soul Stone, he drops her from the cliff.

4. Vision: Thanos uses the Time Stone to reverse the time and kills him after retrieving the Mind Stone.

Here are those who were disintegrated.

1. T’Challa (Black Panther)

2. Peter Parker (Spider-Man)

3. Dr. Strange

4. Bucky Barnes

5. Sam Wilson (Falcon)

6. Wanda Maximoff (Scarlet Witch)

7. Star-Lord, Groot, Drax and Mantis (all Guardians of the Galaxy who were remained before disintegrating)

8. Nick Fury (Former Agent of S.H.I.E.L.D) : Disintegrated in the post-credit scene.

9. Maria Hill (Former Agent of S.H.I.E.L.D) : Disintegrated in the post-credit scene.

As mentionned in the great answer provided by Ankit Sharma, the good guys casualties are:

Loki, Heimdal, Gamora and Vision, by the hand of Thanos himself. With the power of the Gauntlet, you can add Black Panther, the Winter Soldier, Falcon, Spider-Man, Dr. Strange, Groot, Star-Lord, Drax, Mantis, Scarlet Witch, Nick Fury and Maria Hill.

And because you asked also casualties at Thanos' side, we can mention

the death of Ebony Maw, which was expulsed in space by Iron Man and Spider Man while saving Dr. Strange. Correct me if I'm wrong but I think Proxima Midnight got crushed by a huge mechanical vehicle sent by Scarlet Witch. Black Dwarf was sent in the air by Bruce Banner and got exploded, but can't be sure if he's dead. And for Corvus Glaive, he got stabbed but if his link with his spear is also present in the movie, he's certainly alive.

Characters definitively seen left behind at the end of Infinity War include:

• Steve Rogers (Captain America)
• Tony Stark (Iron Man)
• Thor
• Natasha Romanoff (Black Widow)
• Bruce Banner (Hulk)
• James Rhodes (War Machine)
• Rocket Raccoon
• Nebula
• Okoye
• M'Baku

Some characters we don't know about for sure, e.g. Shuri who is not seen after the finger-snap, or Clint Barton (Hawkeye) who does not appear in the movie at all. If you watch Ant Man and the Wasp we also know that

Scott Lang (Ant-Man) survives the event, but appears trapped in the quantum realm

As many people have pointed out, this may have left the entire original Avengers team alive (Hawkeye being in an unknown state) for the fourth Avengers movie that is intended to complete their story-arc, with a smattering of supporting characters from Iron Man, Guardians and Black Panther storylines.