The ancient Eqyptians for me stand out. They pioneered the art of writing, using papyrus reeds to contruct a rudimentary form of parchment to write on and the system of hieroglyphs used forms the world's first known writing system.

They built amazing buildings with very distinctive and ornate architecture and decoration. They coupled the architecture of their buildings with amazing mathematical skills that surpass many buildings even today, depsite being built in an age without calculators or even mass produced rulers. For example, the Great Pyramid of Giza is an immense building, thirty times larger than the Empire State buulding, yet the legnths of the sides of the bases deviate by just 0.0009%. Furthermore, they were aware of the value of pi - the total length of the base sides equal the circumference of a circle that could be drawn if the height was used as the radius. This length is also almost exactly equal to half a minute of a geographical arc at the equator, suggesting that they knew not only that the Earth was a sphere, but that they had calculated the radius of the Earth to 0.004%.

The sides of the pyramid are actually concave, not straight, and exactly match the curvature of the Earth. And finally, the sides of the Great Pyramid are aligned to within 0.058 degrees with north, south, east and west. This wasn't based on a rudimentary compass either, because they face in the directions towards the true poles, not the magnetic poles, displaying an amazing amount of knowledge about this planet.

Their religious culture fascinates people the world over to this day, despite it's use being thousands of years ago and has become for the most part obsolete.

To answer my own question, my favorite ancient civilization is the Mayans. They're mysterious and unique. I've been to one of the old Mayan cities (Palenque) and it was the most amazing place I've ever been. The art and architecture, the Mayan calendar, the still as of yet unknown language; everything about them thrills me.

My favorite is the Romans. They had soo much culture and their way of life was amazing. Of corse like any other civilization their was the dowfall of lots of violence. But the Romans make up for it with lots of other thigs. They had lavish parties, Women really ruled then. Eve though men had the seats in the republic the wome were the ones in control. I just can't describe how much I love the Romans.

The Ancient Greeks because they were the most scientifically advanced.

Vikings were brave sailors ...

The Maya and the Aztecs. They seem so cool, although little is known about them. Mathematically and astronomically impressive feats and uses for the sun and moon. Innovative stuff.

The Egyptians. What an incredibly rich and advanced civilization they were!

HARD question, but I enjoyed reading the other answers.
The Ancient Greeks had a society that produced poets like Sappho. Sure you had to be of a certain social class but there had to be some real positives there.
Still, I might lean towards Rome sheerly out of knowing more about it. (See other Roman answer.)
Any Druids here? I'd like to learn more about them...

I like the Incas because they were the most powerful tribe in South America if not the Americas. They managed to build a sprawling empire all without the use of the wheel. They had a system of counting and measuring and they also had a vast system of roads that stretched the legnth of the empire. Their punishments for criminals were unique although often violent. When they conquored a tribe they didn't force them to be Incas. The Incas commanded their defeated tribes to add certain gods to their worship and demanded tribute, but as long as these criterion were met the conquored tribe was allowed to continue relatively unharmed, eventually they would be completly assimilated into the Incan empire and repeat the cycle. Very interesting people, they had a rigid order to society that seemed to work very well. Without Spanish intervention perhaps they would've conquroed the entire continent.

The ancient Romans built a massive system of civilization. They created modern law and loads of ways to run a vast empire.