Sometimes I see translations of selbstbewusst as confident, arrogant or selfish. I would like to know if this word has a negative or positive denotation. If I call someone of selbstbewusst, is it a compliment or not?
Generally, "selbstbewusst" has a positive connotation and I've rarely heard it used in a negative way.
It could be used as an euphemism for arrogant or selfish, however. Tone and context would help you decide if that's the fact.
Selbstbewusst is chiefly approving.
Er präsentiert[=zeigt] sich sehr selbstbewusst.
If you want to imply that the confidence is rather negative you have to state that the confidence is exaggerated. This is possible by simply saying that the confidence is too much:
Er zeigt sich zu selbstbewusst.
Alternatively you can say that the confidence conveys arrogance or similar:
Sein selbstbewusstes Auftreten wirkt manchmal eher arrogant.
Selbstbewusst may also refer to self-awareness, meaning the ability to get something straight in one's own mind. At an extreme extent this may lead to selfishness.
Still I hardly hear it being used for anything but confident in everyday language while living in Germany. The only common negative connotation was pointed out nicely by Em1.
So in conclusion I'd say that callin someone selbstbewusst can be regarded a compliment.
Context is everything and I'm not a native speaker, so as a result I most likely would consider the entire sentence before concluding as to whether the word's connotation is positive or negative.
EDIT: However, two native speakers have said that they have rarely heard the word with a negative connotation, so take our answers with a grain of salt; it could have a negative connotation, but rarely ever does.
Falls das Wort "selbstbewusst" heutzutage dabei ist, eine negative Konnotation anzunehmen, habe ich es als Muttersprachlerin noch nicht mitbekommen.
Dafür gibt es ja schon selbstzufrieden/arrogant/hochnäsig oder was auch immer. Das bedeutet etwas ähnliches, aber in negativerer Weise.
The answer is: It's something positive. If someone says you are "selbstbewusst" in 99% it's something positive.
Aside: People with the property "selbstbewusst" are human who are sure about their skills and are not afraid to go some risks.
"Selbstbewusstsein": "Knowledge of your self"
Selbstbewusstsein aufbauen etc. is a keyword for many self-development sites and popular books. It's describing the very positive feature. The term is often used in philosophy to describe the state of being aware of yourself, your nature, needs and thinking process (See this wikipedia article).
It's really hard to use it in negative context, to be honest. Well, you can say that someone is self-aware of his needs and therefore egoistic. In the same way you can use words such as assertive in negative meaning. But it comes from people using terms such as self-aware or assertive to justify their egoistic behavior, and not from the core meaning of this words.
Actually the real meaning of the word is more along the lines of
self aware, but in recent years it has mostly been used a synonym for
confident. A tipical example hereof are low-lifes acting
over confident / cocky and being refered to or referring to themselves as
selbstbewusst in a positiv way. This makes the whole expression quite paradox, as overestimating one's own abilities is the exact opposite of
self-aware. Hence, I would say most uses of the term
selbstbewusst are negativ, even if not intended by the person using the word.
If I call someone of selbstbewusst, is it a compliment or not?
While lower educated people do often use it as an honestly meant complement (e.g. you're not afraid of tackling this task), I would be very cautious if an intellectual superior used that word to describe you, as it may mean that you are lacking skills, but at the same time are bragging about begin the best.
To give you an answer to your question: It depends on the social (social class & education) context, but, contrary to the other answers given, it may well have a negativ touch.
A important quote from the wikipedia article on Selbstbewusstsein to back up my statements (please read the whole article, it also gives examples of Kant's and Hegel's holistic interpreations of the word, which do not only focus on the positiv side):
Die affirmative (positive) Konnotierung im allgemeinen Sprachgebrauch des Begriffs verstellt den reinen Wortsinn: Denn ein Modus des Selbstbewusstseins in diesem Sinne wäre beispielsweise nicht nur der Stolz, sondern ebenso die Scham.
Translation (feel free to improve):
The affirmative (positive) secondary meaning (connotation) of this term, which is used in common language, changes its pure literal sense: E.g. a mode of the term
Selbstbewusstsein may not only be proudness, but also shame.
EDIT (some current uses of the term
selbstbewusst, resulting from the discussion):
I found a Ph.D. thesis in the area of artificial intelligence from 2002. In chapter 3.2.6
Selbstbewusstsein is defined very broadly with no hint to any positiv or negativ side effects. You could summarize it, as Eugene said, as seiner selbst bewusst. This logically makes the term self-aware no "false friend" of
selbstbewusst, as it is still used in its literal meaning.