The Klingons have come a long way in the Star Trek universe, starting off in the early days of Captain Kirk as sweaty-looking men with fake tan and stuck on goatee beards. The greater budgets and improvement in special effects made them more alien, with lump bumpy foreheads, pointed teeth and lots of hair, beard optional. This carried forward into the later TV series, and the Klingons have looked that way ever since.
But it's not their appearance that shows the best improvement. Klingons have moved from being sly traders to bloodthirsty warriors to beings with deep honour and loyalty. Next Generation brought this to the fore by having a Klingon officer - Worf - on board, allowing for stories where the race took centre stage, revealing their society and moral code, as well as using them for great plot devices.
For me, the Klingons truly came into their own on Deep Space Nine. Early series portray them as violent and unpredictable, to be approached with caution - on occassion merely for comedy effect. Then Worf arrives to join the crew, and everything changes. Worf was brought in to gain viewer ratings, but it was a masterstroke. The series became darker, grittier, more real (as much as show dealing with a space-station next to a wormhole can be) as war with the Dominion loomed.
More Klingons arrived, becoming regular guest stars as the conflict began, allying themselves with the Federation. Our fearsome warriors were back, but noticeably improved. How? Well, great acting aside, the Klingons were now about who they were, not what they were. Next Generation planted wonderful seeds for this, but it all came to fruition in Deep Space Nine, with sublime results. Stereotypes became characters for the viewer to care about and Worf's shout of "I am a Klingon!" now meant something more than "watch out, I'm big and tough".
Obvious limitations mean that Star Trek's aliens all tend to be bipedal and humanoid in essence - great writing and acting shapes them into people we care about. We'll not only enjoy their company, but mourn their passing when they're gone.