Depending what the most conveniently massive* files belong to, you can sometimes get away with shoving them straight onto another disk.
* If there are just a few things that are huge and easy to find, if you see what I mean.
The easiest tactic is to copy (
cp -ar (
-a is important to preserve permissions etc.)) a directory to somewhere (either a new partition on the HDD or for example a slightly nasty path like
/home/usr/...) then replace the original directory with a symbolic link.
This will mean that anything trying to open them (for reading or writing) in the original location will seamlessly** end up following the link and all will be well.
** ...most of the time
There are some risks in this strategy. If you link out a directory which is part of a software package, you risk the install scripts doing something unexpected on an upgrade and replacing your link, which can leave things half broken. So proceed with care.
It's probably easier to just delete some stuff, though... as most people are saying in comments, it really depends what the space is being taken up by.