Why did this particular show stick with me so much? Well firstly, because it was lots of fun! Although it's got some (okay, plenty) of corny elements and inconsistencies, it still has a rich universe of interesting characters with neat powers, and unlike other shows, maintains some timelessness even now. While it looks dated, it still doesn't look bad. Certain episodes have stellar animation, in my opinion, even by today's standards. Also, even though it had its preachy moments, unlike many cartoons of the '80s, it didn't bludgeon you over the head with a daily moral. (He-Man and She-Ra fans know what I'm talking about here.)
Although I originally watched Thundercats as a child and enjoyed it then, I re-watched it as an adult and still found it entertaining, although for different reasons. As a kid I liked it because it had cool characters and exciting stories that were both fun to watch and act out/play out with friends. As an adult I found it entertaining and got a charge out of the funny lines and the subtext. (Yes, there is subtext, and more than a few suggestive lines, whether intended or not!) Though the show had its share of silly episodes, it also had some with enough depth that someone older than age twelve could still enjoy it.
For specifics on what made an impression on me, read on in these links:

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