In the film version of Dune, (and the novel, AFAIK) the Padisha Emperor conspired with the Harkkonens to eliminate House Atreides- but why did he choose to do so?
The Duke was popular among the other nobles, he had a few troops trained by Duncan Idaho that were almost as good fighters as Sardaukar, and he was very likely to be in the position of making the Fremen his personal fighting force, and the Emperor knew they were likely to be just as good as the Sardaukar.
The Baron only understood the first motive at first, Thufir explains the rest to the Baron later.
"The Padishah Emperor turned against House Atreides because the Duke's Warmasters, Gurney Halleck and Duncan Idaho, had trained a fighting force - a small fighting force - to within a hair as good as the Sardaukar. Some of them were even better. And the Duke was in a position to enlarge his force, to make it every bit as strong as the Emperor's."
Here's the clip from the movie. The relevant portion happens around 1:10
EMPEROR - The Atreides house is building a secret army!... using a technique unknown to us... a technique involving sound. The Duke is becoming more popular in the Landsraad... he could threaten me.... I have ordered House Atreides to occupy Arrakis to mine the spice... thus replacing their enemies the Harkonnens.... House Atreides will not refuse because of the tremendous power they think they will gain. Then, at an appointed time Baron Harkonnen will return to Arrakis and launch a sneak attack on House Atreides... I have promised the Baron five legions of my Sardaukar terror troops.
So we see the scheming as twofold
- The weirding modules the Atreides had developed were considered game changing. Based on the extremes he went to, I'd say the Emperor considered them like we would consider nuclear weapons
- Leto had become popular and the Emperor feared that he would either be undercut politically, or House Atreides would stage a coup and the other Houses would simply allow it to happen.
Leto Atreides was a popular and charismatic man. Moreover, he had assembled a sizable personal army by the time of Dune. He was a threat to the Emperor, especially given Shaddam Corrino had no male Heirs.
He decided to destroy the Atreides by working with Baron Harkonnen. Arrakis was the bait, a prize Leto couldn't refuse, which put him in a position to be killed, away from his home planet.