Here is an example of how to compile and install the latest SVN system in Debian.
At the time of writing the latest stable version was 1.6.17.
Because this method contains all the dependencies of SVN compiling, it can probably be used in many types of Linux distributions. Here are only commands to run as root user without any explanations.

Compilation and Installation

version="subversion-1.6.17"
version_deps="subversion-deps-1.6.17"
wget http://subversion.tigris.org/downloads/${version}.tar.gz
wget http://subversion.tigris.org/downloads/${version_deps}.tar.gz
tar fvxz ${version}.tar.gz
tar fvxz ${version_deps}.tar.gz
cd ${version}
./configure --prefix=/opt/${version} --enable-shared --without-ssl
make && make install
cd /opt
ln -s subversion-1.6.17 subversion
echo '# Set SVN_HOME Variable' | tee -a /etc/profile >> ~/.bashrc
echo 'export SVN_HOME="/opt/subversion"' | tee -a /etc/profile >> ~/.bashrc
echo '# Add SVN_HOME/bin to PATH Variable' | tee -a /etc/profile >> ~/.bashrc
echo 'PATH="$SVN_HOME/bin:${PATH}"' | tee -a /etc/profile >> ~/.bashrc

Checking the newly compiled SVN system.
source /etc/profile
svn --version
Result should be:
svn, version 1.6.17 (r1128011)
compiled Jul 25 2011, 15:10:49
.
Copyright (C) 2000-2009 CollabNet.
Subversion is open source software, see http://subversion.apache.org/
This product includes software developed by CollabNet (http://www.Collab.Net/).
.
The following repository access (RA) modules are available:
.
* ra_neon : Module for accessing a repository via WebDAV protocol using Neon.
- handles 'http' scheme
* ra_svn : Module for accessing a repository using the svn network protocol.
- handles 'svn' scheme
* ra_local : Module for accessing a repository on local disk.
- handles 'file' scheme
* ra_serf : Module for accessing a repository via WebDAV protocol using serf.
- handles 'http' scheme
- handles 'https' scheme