I'm looking for something along the lines of K-9 for my phone. Does such a thing exist?
My goal: to have all adult content blocked.
I would like to know if this is possible and if it is, how to do it.
If you have a rooted phone, you can always edit your hosts file to block known adult sites.
Trying to block all sites is an exercise in futility, unless you opt for a slight reversal of logic and use white-listing wherein only allowed websites are allowed to be connected to and all others are blocked. As of now, I'm not aware of any app on Android that offers this functionality.
There are other avenues for adult content - the Android Market is one of them and blocking that seems counter-productive for a smartphone.
Also take a look @ DroidWall - an app that only allows certain apps to access the Net.
*UPDATE:*Trend Micro's paid app Mobile Security seems to have parental controls, although I can't vouch for the app's efficacy. The user reviews don't paint a very comforting picture but a 30 day trial is available so you can test the app out yourself.
It doesn't block content, but X3Watch monitors what websites you visit. If you use that in conjunction with DroidWall as suggested by Sparx, or use an App Protector to block/limit other apps, that may help.
Update: Covenant Eyes now has an app now available in the Market. As with X3Watch, it doesn't block sites (though it may in the future) but reports what websites you visit. It is officially a beta version, but seems to work well. The app itself is free, but usage requires a Covenant Eyes account - which also covers usage of any programs on the PC or Mac.
K9 Webprotection is out for Android.
Seems like it does not work for some devices, though, as it's based on Firefox.
This can always be combined it with an app locker to block the default Chrome browser.