Baka(バカ) is probably the most popular Japanese "swear" word. Nothing is immune to being "baka." In some places, baka is like saying "shit" or "damn" in the US, but in other places, it still carries a harsher meaning and can be pretty insulting.
Baka is thought to be an imported word, though where it came from is highly despuitable. Some Japanologists believe it came from China via the sandskrit word "moha". Others feel it orginiated with the Ainu word for idiot, "paka". It's even been suggested that baka is an Indian extraction of the Hindu insult "bakwa".
Where ever it came from, it means the same thing; someone or something is stupid.
Baka first appeared on paper in the 14th century, though some scholars claim to have traced it back even further to the Heian period (794-1185). Back then, the word was "waka", which means "infantile" or "simple minded". However, in these modern times, it is known as "baka" or "bakabashi" (idiotic).
There are many uses for the word "baka". It can be applied to anyone or anything. The word has no limits. For kicks, lets look at some examples of how to use the word "baka":
(remember; japanese syllables are formed by using a consanant and vowel, or a vowel(s) together (no more than two at a time). The exception is the syllable "ん" or "n". Vowel sounds are as follows: "o" as in "corn", "a" as in "father", "e" as in "prey", "i" as in "keep" but shorter, and "u" as in "lute". "ん" or "n" is held for one beat, meaning it is it's own syllable.)
If someone is stupid:
ばかじゃん！
baka jan!
(what an idiot)
お前ただのバカものだ！！
omae tada no bakamono da!!
(you are such an idiot)
くせバカチンだよ!
kuse bakachin da yo!
(He's a fuckin idiot)
If something is stupid:
バカみたい!
baka mitai!
(This is stupid!)
If someone is being stupid and you want them to stop:
バカやめろよ!
baka yamero yo!
(don't be such a moron!)
バカ言ってんなよ！！
baka itte n na yo!!
(don't say such stupid stuff/don't talk shit)
Of course, baka isn't the only way to express stupidity. There are several other words in use, such as the popular Osaka term, aho (アホ）. Aho too means someone or something is stupid.
お前アホだよ！
omae aho da yo!
(your a moron!)
このアホ!
kono aho!
(you dumbass)
And for giggles here's a few other zingers alive and well:
アホンダラ
ahondara
(idiot)
タワケ
Tawake
(idiot)
ノウタリン
notarin
(airhead)
ウスノロ
usunoro
(simple minded/slow)