If you look up 「切れる」 on Jim Breen’s WWWJDIC, you will get a huge list of definitions.

切れる 【きれる】 (v1) (1) to cut well; to be sharp; (2) to break (off); to snap; to wear out; (3) to be injured; (4) to burst; to collapse; (5) to be disconnected; to be out of; to expire; to sever (connections) with; (6) to be shrewd; to have a sharp mind;

Some of these, I would take with a grain of salt. For instance, I have no idea how you would use 「切れる」 to mean “to burst”. Nevertheless, 「切れる」 has many, many uses which you might want to become familiar with.
For instance, what if you wanted to say something ran out or expired?

１）電池が切れるから、新しいのを買った方がいい。
– The batteries are going to run out so you should buy a new one.

２）この商品はもう売り切れです。
– This item is already sold-out.

３）賞味期限がもう切れたから、捨てた方がいいよ。
– The sell-by date has already expired so you should throw it out.

Or what if your connection gets cut off such as on the phone?

１）トンネルに入ったら、電波が届かなくて電話が切れた。
– Once entering the tunnel, the signal didn’t reach and the phone got cut off.

You can even use it for when you lose your temper.

１）もう我慢できなくて、切れた。
– I couldn’t take it anymore and I lost my temper.

Perhaps, one of the most useful thing about 「切れる」 is that you can take the negative and use it as a verb suffix for things you can’t cut off and put an end to. This is the same as the expression 「切りがない」 for things that have no cut-off point and seems to be endless. As you can see by the examples, you just take the stem of the verb and attach 「切れない」 .

１）こんなにたくさん食べきれない。- I can’t eat this much.

２）どう頑張っても、この宿題は絶対やりきれないよ。
– No matter how much you try, there’s no way you will finish this homework.

３）状況はまだ把握しきれてないため、明日まで検討させてください。
– Because I haven’t finished getting a handle on the situation, please let me find things out until tomorrow.