Archer: We're all ruled by our vices, and will always make poor decisions because of them.
Avatar: The Last Airbender : War Is Hell, and forgiveness, love, friendship and compassion win out over spite, hatred and fear in the end. A friend may become an enemy, but an enemy may also become a friend. Destiny is choice - and choices must be made, not put off.
The Legend of Korra: Attaining balance, whether it be in an individual, a city, or the world. Recognising one's own strengths and weaknesses, and by doing so, adapting to your personal environment and situation.
Ben 10: Make the best out of the cards you are dealt.
Family Guy: Family sticking together despite their differences.
Frozen: Familial love can be just as strong, if not more so than romantic love.
Futurama: Loneliness. Difference. Some ideas remain familiar even after the world has changed enough to become unrecognizable. No matter how different and isolated you are, you can always find common ground with people if you look for it.
Gargoyles: The evils of bigotry and prejudice, and the importance of acceptance. The value of family, both the family you're born into and the one you choose. If you dedicate your life to vengeance you will bring nothing but pain, both to yourself and to those around you.
Hey Arnold!: People in poor circumstances finding happiness.
Ice Age: Friendship, forgiveness, redemption, and how the actions of one innocent person, kidnapped for the slaughter, can transform a trio of misfits into a true family. Love and forgiveness can create harmony in spaces where sin has crept in. Love is shown through acts of sacrifice/sacrificial love.
Luckily, the aliens are morons, too. Word of God points out that anyone with the Irkens' miraculous technology and average intelligence could conquer the Earth in no time. Zim, on the other hand, is continuously thwarted by his own ridiculous plans, a complete lack of common sense, and a ten-year-old social outcast; the aliens in "Abducted" are utterly brainless. One could argue that Invader Zim contains a subtler theme that technology makes us stupider because we no longer have to think.
Teen Titans: The central theme of the whole show is The Power of Friendship. Several of the season arcs are centered around the theme that you may be Not So Different from a villain, be it by blood, abilities, or personality, but you can always choose to be a better person. The Terra arc also has the central theme of taking responsibility for one's actions, and the Raven arc says yes, you canScrew Destiny.
The Simpsons: Family will always stand by you and accept you for who you are, no matter how much you fight, how different you are, or how crazy you drive each other.
For Springfield in general: Everyone in the world is unique and seems a little insane to everyone else. You won't make them change. Get used to it.
For Springfield Elementary: The educational system is flawed and so are the people in it.
ThunderCats (2011): Right Makes Might. Being a proud badass doesn't make you a good leader. Seeing the big picture, having clarity, doing what's right, and showing kindness, selflessness and mercy towards all does make a good leader, and is the best way to combat the evil in the world that would exploit people's hatred and selfishness.
The Toy Story series as a whole: Growing old and confronting your insecurities and mortality.
Toy Story 2: Confronting your mortality and deciding how you will live your life because of it; is it better to take risks if it means you'll get damaged or even killed, or to live the safe life — and is the safe life really living at all?
The second film also has choosing between long-lasting, superficial admiration or a genuine, fleeting relationship.
Up: Life is an adventure. Don't let grief and bitterness keep you from it.
The Venture Bros. is about failure, and failed expectations in particular. The setting is a failed Used Future take on the Space Age ideals, Rusty Venture and Billy Quizboy are failed child geniuses, and almost every episode is about how some experiment crashed and burned.
The writers go into amazing detail. One character, Pete White, is a failed super-scientist. He lives in a trailer, the typical home of failures. The trailer itself is on bricks, meaning it can't move like trailers should. Near his home is a billboard informing the viewer that the trailer is the only house of a planned subdivision. The establishing shot takes up only a few seconds, and we know the character is a failure, his home's a failure, and the ground his home is standing on for miles around is a failure.
Wakfu: If you have the power to help somebody in need, then you should, that's what makes a hero.
WALL•E: Even in the bleakest of scenarios, love can renew life.
Also, people need to stand on their own two feet and take care of themselves to make a life worth living.