Yes it will run Java, but big stuff is going to end up being slow due to the limited RAM. You'll need to install the JDK package.
Technically you should only need a JRE (Runtime Environment) package to run Java which is smaller than the JDK at least in terms of download and installation. You should only need a JDK (Development Kit) if you want to compile your own programs on the Pi. The 'beauty' of Java being the ability to develop write-once-run-anywhere.... Ha Ha Ha Ha.
Sun developed something called CVM which is a lightweight, stripped-down Java virtual machine supporting the J2ME specification. It doesn't offer the full library support of a standard J2SE JRE but could still be useful. Plus I know it ran on ARMv5 so may be avaialble for later ARM chips.