There's an interesting discussion on Alas: 'Is The Oppression of Women The Root Of All Oppressions?' Now I've given my response to that argument in the comments (Short Answer: Don't know, don't care. Slightly Longer Answer: Will you shut up with comparing black men to white women already; I'm glad that the rest of us have learned a bit from the 19th Century), but I thought I'd take this opportunity to write a little about why I just call myself a feminist, and don't put anything before or after it.
If you read any introduction to feminism, or introduction to political science, it will usually contain a description of the different types of feminism. The big three, that are almost always included, are: liberal feminism, radical feminism, and socialist feminism. Then you might also get anarcha-feminism, lesbian feminism, third-wave feminism*, eco-feminism and so on. It might look something like this
Liberal Feminists: Believe that if we all just gained formal legal equality then it'd be hunky dory. Are rather lame. Want all women to go out to work and don't necessarily like mothers very much.Ok they may not look exactly like that, but they can be about that simplistic; they give the idea that feminists all fit into 3 (or 8 or whatever) groups and they organise along these lines.
Socialist Feminists: A bunch of communists who look at class as well as gender. Don't like blaming men for things. Will often ignore things men are responsible for. Want to work with men, because they want men to like them.
Radical Feminists: Believe women are the first and most important group to ever be oppressed. Hate men, and sex. Like hippy women-only events that will never change anything.
I actually think this is fundamentally inaccurate. I know a bit about the New Zealand feminist movement, and while at sometimes some women organised themselves into groups on this basis, the majority of time they didn't, particularly in the early 1970s. Now I know that it was slightly different in America where NOW was formed completely seperately from the women's liberation movement and the two existed as two seperate strands of feminism. But I still think you can overestimate the usefulness of that sort of scheme as a way of describing feminists and feminist action, as opposed to feminist theory (the writers of which, I believe, are more likely to fit this scheme, than your common or garden feminist).
I think feminists tend to take a little from column A, a little from column B, and use it analyse the situation they're in. For example, in New Zealand in the early 1970s feminists (of all stripes) agitated for a motherhood wage (this was a solution to the reproduction problem that was more important, and developed earlier, in New Zealand than anywhere else). It actually got to the stage where the 3rd Labour Government (slogan: If you think we're bad wait till the next one) proposed a motherhood wage at about $10 a week (more money than it seems - I don't have my wage calculator on me but I think it'd be at least $100), which would be funded by cutting the family benefit from women who were working. Now there are a couple of different accounts of feminists' reactions to this which compare one reaction (usually called the liberal reaction) which said that the amount wasn't enough, and another reaction (usually called the radical reaction) that said that it would force women to continue to carry out child-care roles. But if you go back to the source material you see that feminist groups of all different sorts were making exactly these two criticisms (and a third criticism that it wasn't ok to make women who looked after children in the home richer by making women who worked outside the home poorer).
I think if people self-identify as a certain type of feminist, more power to them, but I don't believe this sort of scheme covers the feminist movements, or feminists particularly well.
That's not the reason I just call myself a feminist, but it's an important piece of background.
I don't call myself a radical feminist because the argument about primacy and firstness of oppression bores me. On a more philosophical level I don't think you need to add the term radical to feminism - the word makes it very clear that it's looking at women, what could go more to the root than that?
As for the other terms they are all coupling feminism with another theory, each with it's own history and each of which was developed by men who often forgot women existed. I don't believe you can take a long standing theory add a feminist analysis and hey presto both are enhanced. There's an article called 'The Unhappy Marriage of Marxism and Feminism' which says that Marxism and Feminism became one and that one was the husband. I don't think feminism needs to be married to any other theory in that way.
As feminists we do need other forms of analysis than feminism, the world is a complicated place, and gender isn't the only thing affecting women's lives. But I don't think they need to modify our feminism. Our feminism can stand on it's own two feet.
*I've always found the term 'third-wave' feminism unsustainably arrogant. It was bad enough in the 1970s when women called themselves second-wave feminism (ignoring all the feminist work that happened between winning the vote and the 1970s), but they didn't know about women's history because that history had been buried. We now know about the history of post-suffrage feminism. To say that a third-wave has started already implies that what's going on now is more significant than anything that happened between the first and second wave - which is simply not true.