Creating aliens is hard in any venue. To really be alien a being has to differ from humans in some fundamental way. Otherwise you're just slathering latex on your actor's forehead or renaming orcs and elves.
One of the most obvious ways to create an alien is to give them telepathy. As humans we are used to saying one thing and meaning another (lying if you want to be uncharitable). We communicate through a flawed and complex medium called language. We are sometimes unclear. Telepathy cuts right through the bullshit. You can say what you mean. On the downside you say what you mean.
The medium of telepathy is not given enough development in most settings. When you and another are communicating mind to mind to you hear voices in your head? Can you send a mental picture? Are the exchanges like memories you suddenly can access? That in itself can add a lot of color to a scene. As humans we live in two worlds, the outside world and the one in our heads. What happens when you blur the line between the two or when you can invite someone in to look around?
Consider psionics in Traveller. The designers wisely limited their use through psionic points. You can't walk around scanning people's minds for their pin numbers constantly. You'll burn out in a few minutes. Of course that could be enough if you're on the stock exchange or sitting near the right minds.
So the Imperium that has fought the psionic Zhodani for centuries developed the psi screen (TM). This helmet like device holds a disembodied weasel brain in a portable life support system. The weasel brain's constant primal thoughts of fight/flee/hunger/sleep/mate drowns out the wearer's own thoughts. The helmet is regarded as a major improvement over strapping a live weasel to one's head (TL 0, or TL 1 for a brass cage it can't chew its way out of).
It does raise interesting possibilities. A planet where some humans are psionic might see people flocking to grab pets for their value in screening their thoughts. Or on a world with restricted psionics, sensitive humans might be required by law to always have such a pet present. Some actual folklore holds that having animals around will shield a person from curses and black magic (dirty trick to play on the animals though). Perhaps a diligent referee will take these legends as accounts of psionics being foiled by man's best friends. Yes I'm including cats. I'm pretty sure they think more than dogs when they're awake. I'm guessing birds or higher mammals would be needed to shield your thoughts.
Having no defense against telepathy would usually mean a dictatorship and you might not even realize it. The term 'conspire' means to 'share breath' referring to people sitting together closely and whispering about their plans. We don't even have a term for the degree of closeness telepathy allows. Even a weak form of it will allow people to meet clandestinely anywhere. No bugs, no wiretaps will ever find them out. We won't even know they're meeting. In fact a meeting might see members spread across a city or nation with powerful enough mind links (not to mention if they used crazy homeless people as booster stations).
More tellingly you'd never be able to betray these people. They could subject you to a scan to determine your true intentions at any time. There'd be no infiltration and traitors from within would not last long. Of course everything I'm saying needs to be taken with a grain of salt. No system is perfect and telepathy can do whatever you want it to in your setting. Perhaps some people can screen their thoughts or even set up fake thoughts (like a player character). Maybe a courageous AI tries to free its makers and is branded a rogue machine by the secret masters ("Why did you even order that android built?" "Me? I thought you did!" "Okay who ordered it built? We all sound alike in mind speak!" "Haha!" "WHO SAID THAT?!") Fighting a telepathic conspiracy in a campaign is enough to make anyone paranoid, especially if you add a little mind control to the mix. Not being able to trust your friends is one thing. Not being able to trust yourself is a whole other level.
Edit: The part about disembodied weasel brains it turns out is not from Classic Traveller. If anyone can tell me where I read that I'd greatly appreciate it. If it is my own idea even better because it opens up epic plot hooks!