Most applications do need to be installed by admin because, I believe, they need access to system resources or files otherwise protected from accessing or modifying.
At the same time, for example, Netbeans or Aptana do not need to be installed by an admin (both use JavaRE).
So, three questions:
1) Is there any more or less general method of installing applications from a repository without using sudo by a non-admin user for her only use? At least those applications that do not require anything special to work.
2) What other applications/games etc. that do not require to be installed by admin do you know? (I have no idea how broad this question is.)
3) When a Java-based application is installed by a non-admin user, does it (JavaRE) give the application access to any system files/resources etc. otherwise protected from modifying? I would think no, but at the same time Java was installed by admin, and during installation it may have granted itself access to some resources.