Most of these are liberal/progressive, because that's what I am. If you want to become more active, any of these will be more than glad to help. If you just want information, you can find that here, too. These are presented in no particular order, and this is far from an exhaustive list. It's just some of the ones I find most helpful.
The League of Women Voters - Very old, very respected, and fairly unbiased. This site is full of sound information, especially if you want to compare candidates, and so on.
People for the American Way - Established more than 25 years ago, People For fights for equality, freedom, and justice for all. (And by all, they mean all, not just "all the ones like us.")
Civil Rights.org - This is the site for The Leadership Conference on Civil Rights; the oldest (and largest) civil rights coalition in the US. It was founded in 1950, and is comprised of over 200 Civil Rights and Human Rights groups. Also collaborating on the site is The Leadership Conference on Civil Rights Education Fund, which was founded in 1969, and produces educational materials, tracks court cases, and watches law enforcement for the LCCR. If you want to know anything about civil or human rights in the US, this is the place to go.
Human Rights Watch - Watching the globe for human rights violations, and shining the spotlight of media attention on them, to hold those responsible accountable for their actions. The Human Rights Watch has been doing this for 30 years, and the world is a better place because of it.
Amnesty International - Also watching the whole planet, and reporting abuse, helping political prisoners, standing up for women, children, and other minority groups, and fighting for a world in which everyone is treated with respect. They have chapters in many countries, and millions of members; so if you are interested in helping, there's a place for you here.
United for a Fair Economy - UFE (in their own words,) "raises awareness that concentrated wealth and power undermine the economy, corrupt democracy, deepen the racial divide, and tear communities apart." They fight for equality, to close the "wealth gap", to educate, and to bring people together. If you're unaware of what it does to workers when the people at the top of the company take home more in a single day then the lowest paid worker can earn in more than a year (which, by the way, is the average gap among large corporations in the US) then you should read some of the articles here.
Southern Poverty Law Center - Founded in 1971, the SPLC works through education and legal action to help those who are most at risk in the US. They've been keeping an eye on the growing number of hate groups since 1981. If you've encountered organized hate, and you are concerned about it, you can come here for help.
Teaching Tolerance - this is the Education branch of the Southern Poverty Law Center. Hate and fear thrive on ignorance; the SPLC provides educational material, free of charge, to combat that ignorance. If you're an educator, whether or not you're in the US, and you'd like some materials to help teach tolerance in your classroom, (or if you're a parent interested in teaching tolerance to your kids,) this is the place to go for stuff that's won 2 Oscars, an Emmy, 2 Golden Lamps, and dozens of other awards and honors.
American Civil Liberties Union - The ACLU is, perhaps, the most well-known civil-rights organization in the US. They've been fighting tirelessly, in the courts and in the media, to protect the rights guaranteed by the Bill of Rights, and often denied to minorities of all stripes. Many people think that they go overboard at times, and perhaps that's true. But the thing about rights is that they apply equally to us and to those we disagree with, or even those we suspect would do us harm. Sure, it would be easier to deny people who hate us, or would take advantage of us, their rights and their humanity; but if we can do it to them, then they can do it to us, and then where will we all be?
Council for a Livable World - This group, based in Washington, DC, works to reduce stockpiling of nuclear weapons, and for sensible national security policies. It was founded by nuclear physicist Leo Szilard in 1962 to act as the "sweet voice of reason" to explain the dangers of nuclear weapons, and to stop the arms race. The organization is still doing that, by working hard to help reasonable men and women get elected to Congress, and to educate the public about nuclear weapons.
MoveOn.org - One of the most influential progressive sites, MoveOn™ works through the internet to make grassroots political movements more powerful, and more accessible to everyone in the US. If you have limited time and resources, but you want to make a difference, join this group. You'll get Action Alerts, news, and other ways to keep an eye on things, and you'll be able to join your voice with the voices of millions of others. Together, we can change the world.
True Majority - founded by Ben Cohen (of Ben and Jerry's Ice Cream) this is a grassroots organization that uses the internet to promote social justice, help kids get a good start in life, protect the environment, decrease military funding, and get America to work in harmony with other nations, as part of the global community. It's free to join, it's fun, and they've been known to give ice cream to people who are especially active!
MomsRising.org - An organization that seeks to change the unnoticed and unquestioned bias against mothers, especially single mothers, that exists in the US. We are the only industrialized nation with no laws about sick time, maternity/paternity leave, or equal pay for equal work. There are no programs in place to ensure basic health care for all our children. There is nothing to help single parents care for their children while the parent is at work. Because of this, one quarter of families with children under six years old live in poverty in the US. Fourteen million kids are unsupervised after school, including 40,000 kindergarten students. We have one of the highest infant mortality rates in the developed world. MomsRising, started in 2006, is seeking to combat all of this through grassroots organization and activism.