Here's the relevant passage: "He (Elisha) went up from there to Bethel; and while he was going up on the way, some small boys came out of the city and jeered at him, saying, "Go up, you baldhead! Go up, you baldhead!" And he turned around, and when he saw them, he cursed them in the name of the Lord. And two she-bears came out of the woods and tore forty-two of the boys." (2 Kings 2:23-24)
There's a lot of misconceptions about what happens here, some through an understandable misconception of the situation or the wording, and some through purposeful twisting of the events here.
First of all, the bears did not 'eat' the people in question (as critics usually say), but 'tore' them. It may sound minor, but eating them is fatal, and tearing them is not necessarily fatal. It's possible that none of them died.
Also, Elisha didn't send the bears out. He merely cursed those telling him to go up. God apparently decided to send the bears out.
Also, those who were mauled weren't children. Though the KJV translates their identities as 'small boys'. The Hebrew phrase here 'neurim qetannim', can refer to men from twelve to thirty years old. The soldiers in 1 Kings 20:14-15 are 'neurim qetannim'. Some people assume that Elisha was much older than them, since they called him 'baldhead', but he was actually in his mid-twenties himself, making him a 'neurim qetannim' as well.
On top of that, these men weren't merely 'teasing' Elisha. We know that there were at least 42 of them, probably several hundred (since it's unlikely that only two wild bears could catch the majority of the people in any group). Several hundred people chanting against a single man is not 'teasing', but a clear threat. And their telling him to 'go up' doesn't mean 'get out of here' as the critics seem to be suggesting, but means to die. They knew he was a prophet of God, and are telling him to die and go up to God. If you had several hundred people telling you to die, would you consider that teasing? No, Elisha was clearly in mortal danger, and God sent the bears out to save him.
See also: Christian Thinktank: Mean, Mean Elisha