See an article on Minecraft and Kid's internet Safety here and CommnSenseMedia's take on the safety aspects of Minecraft for kids here.
To address these issues, a few companies, including myself, have created family-friendly, kid-friendly, servers that are either moderated, or which block offensive content.
I, a technology teacher, and writer for this blog, have started a Minecraft server that blocks swearing, and is reviewed for appropriateness. Membership is 120/yr for access which includes op enabling for players and multiple creative worlds. Parents must skype ahead of time to prove identity of themselves and their child in order to block adult access (except parents who are welcome). Additionally, conversations can be held on Teamspeak, an audio-communication tool (free) where parents can monitor communications. click here to sign up for more info: https://docs.google.com/forms/d/1k-j2BJsiwYZheXGsGcFVpp3S8YfPm8VUc9QnFS5oKtc/viewform
Another option is Intercraften:
"Our main goal is to maintain a safe place for kids to play Minecraft. We are "semi-vanilla," meaning we try to keep things as close as possible to the way Mojang intended the game to be.
We are a "legit" PvE survival server, meaning everything you see in our world was mined, grown, smelted, crafted, built, and/or created by a player. Nothing has been nor will be spawned into the game by illegitimate means. Players also do not have to worry about being attacked or killed by other players.
Our chat is censored for language and attempts to bypass it are met with swift action and removal from the server. Players can very easily lock their chests and protect their own builds from griefers and thieves.
We offer three worlds to play on, one of each difficulty (easy, normal, and hard). Everyone begins with access to the easy and normal worlds, and can gain access to the hard world after some time on our server."
The city center and games area (Hunger Games roof) is non-PVP. The Biomes and outside the city are all PVP enabled Anything you build outside of a plot you buy is not protected unless it is in a faction. Chests are protected, the rest is not. It isn’t “griefed” if someone moves in and re-decorates it with a pickaxe. I won’t fix it. I won’t kick someone out of your area in the wilderness. If you want protected areas factions are an easy way to do that until you can afford a permanent city plot.
If you want a protected area, buy a plot or start/join a faction.
You earn money and experience mining, building and killing mobs. Most every block can earn you money so have fun.
There are many chest shops for you to buy and sell things you have, mine or want. Shops are in the tower. Take the stairs. You can sell the diamonds which you can earn every day for voting.
There are signs and portals everywhere on what you can do, especially when you get out of spawn. Read them!
Actual Cub, Girl and Boy Scouts get entry into the Scout only room at spawn. They also get special commands, shown in the room.
Rule 1: No griefing, hacking or flying. (really we have jail and ways to check)
Rule 2: Now whining or asking for stuff. (that includes mod, rights, gifts, etc.)
Rule 3: No PVP in city except PVP areas. (It should be protected but if we see you anyway…)
Rule 4: No Swearing.
Rule 5: Have fun
A Family Friendly, Kid-safe Minecraft Server for PVP:
Server Maps: http://minesquish.indiesquish.com/maps/
Server Rules: http://minesquish.indiesquish.com/minesquish-server-rules/
Jupitercraft: An Australian Minecraft server banning swearing, griefing and other bad conduct can be found here: