Not existing; the state of something not being there or not existing.
部屋に証拠は何もない。
There is no evidence in the room.
彼の名前はリストにない。
His name is not on the list.
この商品はもう在庫がない。
This product is no longer in stock.
Not owned; not possessed — indicating lack of possession or ownership.
今、車がないので電車で行きます。
I don't have a car now, so I'll go by train.
彼はまだパスポートがない。
He still doesn't have a passport.
私は兄弟がいない。＝兄弟がない（※一般的には「いない」を使う）
I have no siblings. (Usually said as 「いない」.)
Unique; unparalleled — indicating something extremely rare or one-of-a-kind.
こんな機会はまたとない。逃すわけにはいかない。
An opportunity like this is once-in-a-lifetime. I can't miss it.
彼の才能は唯一無二で、代わりがない。
His talent is unique and irreplaceable.
これはまたとない美術品だ。
This is a priceless (one-of-a-kind) work of art.
Used in structures like '〜ことがない' to indicate that something does not/will not happen, or that one has no experience of it.
彼が遅刻することはないと思う。
I don't think he will ever be late.
そんな失敗は二度と起こることはないだろう。
That kind of mistake will probably never happen again.
私はその映画を見たことがない。
I have never seen that movie.
Used after the stem of an i-adjective (〜く) to form the adjective's negative (e.g. 高くない = not expensive).
このケーキは甘くない。
This cake is not sweet.
今日は寒くないから、コートは要らない。
It's not cold today, so I don't need a coat.
この問題は難しくないよ。やってみて。
This problem isn't difficult. Try it.
Attaches to the -te form of verbs to form '〜ていない/〜てない', indicating non-existence of a continuing state or that something has not been done.
彼はまだ帰っていない。
He hasn't come back yet.
宿題、もうやってないの？
You haven't done your homework yet?
その話は聞いていないから、知らない。
I haven't heard that story, so I don't know about it.