You should not install it without formatting the root partition. That's because it will overwrite the files, but if there are some files that don't exist in the new system, they don't get overwritten and you get garbage left on the disk
If you partitioned the wise way last time you installed, and have a separate /home, you can just go about installing - do manual partitioning, check-box the root partition to be formatted, leave others (like /home) unformatted and just make sure they get mounted the right way (home partition mounted as /home and so on). After setup the thing should be going good.
If you did "automatic partitioning" or something, you probably only have root partition (in addition to swap). In this case you can't format it without losing your personal data too; you need to take backups that you put back later. To get your users' personal data backed up, copy (recursively, including the hidden files and such) the /home directory which holds all user data unless you've specifically copied things to other places (in that case you know where they are, and can copy them too). Then there are the system-wide configuration files, which are placed into /etc and so on. From these you only need to backup the ones you have altered after the setup; others you don't, because the new system will likely have more or less the same defaults. If you haven't touched anything, you don't need to copy anything except for /home.
It isn't a bad idea to collect the configuration file names you modify into a list that you can later use as a check-list when you make backups. /home you usually backup completely, so there's no trouble there, but the system-wide things should be written down if you make changes; maybe even a script that you can then run before updating, which copies all of them into an archive or something, preserving their paths - so after reinstallation or upgrade you can just extract the archive to the root of the filesystem and have the files put into their places.