What does the phrase “I’m down with” mean?

I was wondering about the meaning of:

I am down with something.

Also, I was wondering whether people say:

I am up with something.

If so, what does it mean?

If you are down with something it means that you have knowledge of something or are in agreement with it. I'm down with science means "I am familiar with science" or "science is a good thing." To be down with something is a slang phrase, and not terribly common in formal speech or writing.

You could also speak of having a disease, sometimes preceded by the verb to come if the sickness hasn't yet fully taken hold. eg. I am coming down with a cold. or She is down with the flu.

To be up with something is only used in the imperitive, eg. up with the king! — meaning hey, that king is pretty great. Or: up with ice cream! (Yay! Ice Cream!) You would never say I am up with something. That wouldn't be proper english. Although you could say I am up to something, you sneaky little devil, you. (In case it's not clear, "I am up to something" means "I have an ulterior motive I don't wish to reveal.")

If you are addressing someone directly who is presently seated, you could use a command: up with you! (stand up.)

Other than a literal interpretation I am down/up [here] with a hammer (and this would be rather questionable with regards to grammar), "down with" is slang for a handful of subtly different meanings.

I am down with [subject].

I am down with [person].

I am down with that.

I am down with [location].

More often than not, these mean "I am in agreement with" but the type of object matters quite a bit.

I am interested in and think this subject is cool.

I really like that person. (Platonically.)

I am ready for that / I can do that / Let's go do that

I like this location / That location is good

I am not familiar with "I am up with". It would not surprise me to hear someone using it as a slang version of "I am down with" for emphasis. "I am so down I am up."

More commonly, both phrases can be used with "for" in place of "with":

I am down for some pizza

I am up for a movie

If the 'something' is an illness or malaise, then "I am down with the lurgy" means that I am suffering from an illness and normally that I am in bed and hence not getting up, so staying down.

I don't think I've ever heard anyone say "I am up with something". In a wholly different context, "I am up on something" means I've studied something and know something about what it is all about.

Stating that you are "down for that" appears to be a relatively recent phrase coming from slang. It is common in chat rooms and other online social hangouts, but does not often appear in writing. It shocked me the first time I heard it (sometime in 2013, if I remember correctly). I thought the speaker was confused, at first, until I heard it repeated in different contexts and came to understand that "up for that" and "down for that" have approximately the same definition to most people.

Years ago (and the number of years is unclear to me) being "down with something" had a different meaning on the street, or amongst those who were less... formal. It meant that you were involved in something seedy, or had inside information on something. "On the down low" shares some of the same connotation, where you are describing/referring to something out of the public eye, unknown to the wife/girlfriend, or otherwise a secret.

Being "down for that" implied not only that you agreed with someone, but that you would keep your involvement a secret. Conversely, being "up for that" was an open acknowledgement of your agreement or participation; it was not private, and no secrecy was implied or conveyed.

Because English is English, and slang moves into the mainstream if it gets enough attention, they now mean the same thing. It still makes me cringe when I hear it, however, just as I do when people use "irregardless".