'The Alien', which I've been talking about a lot lately, was of course a man (a 7-foot Masai) in a rubber suit, lifted above the banal by alien biological extras and the strategic use of shadow and mist.
Other media triumphs include the Daleks - men in suits but not man-like. I'm not a massive fan but they annexed the public imagination.
The trek franchise had a few decent non-humanoid aliens. I think perhaps the best was the silicon-based lifeform in the original series. That had a fully alien biology, and the story was about trying to communicate across this difference.
The Andromedans in Blakes 7 are the same creatures as 'The Thing', but their threat is political rather than visceral.
So, in short, it is possible to convey interesting, alien, aliens, even with a limited special effects budget. But it isn't done very often. Any other suggestions?