Set DNS by Mytechie
This app lets you easily define the name servers used by your Wi-Fi and mobile network interfaces. You can speed up browsing, enable content filtering, or bypass DNS-based filters by using a third-party DNS service. Android lets you natively change the DNS server addresses for just the Wi-Fi interface and is only available if you define static IP information. However, Set DNS lets you change both interfaces and can work when using DHCP.
When you open Set DNS, you can easily select input custom DNS addresses, or select from some popular free DNS servers: Google DNS, OpenDNS, OpenDNS Family Shield, and FoolDNS. Then to activate, you'd simply tap Menu > Preferences and then choose the Locations (interfaces) you'd like to enable it for.
The Pro version of Set DNS ($1.58) lets you set a password in the app to lock down the name server settings and preferences. It also includes widgets that you can add to a home screen to quickly view and change the DNS state.