I'm looking for an application which allows me to see what is consuming the most disk space and also to delete the files from there.
My personal favorite is GNOME Disk Usage Analyzer (baobab):
You can install it with
sudo apt-get install baobab
Select any file from the table on the left side to move it to trash on right click.
Personally I like KDirStat
you can install with
sudo apt-get install kdirstat
If you're using KDE, I'd recommend
You may install it using:
apt-get install filelight
It is very similar to GNOME baobab recommended by terdon.
The wikipedia entry says:
Filelight is a KDE graphical disk usage analyzer, part of the KDE Utils package, which uses the sunburst chart technique to display disk usage. Instead of showing a tree view of the files within a partition or directory, or even a columns-represent-directories view like xdiskusage, it shows a series of concentric pie charts representing the various directories within the requested partition or directory and the amount of space they use1 (this method being known as a sunburst chart, ring chart, or multilevel pie chart).
A user may also click on the pie chart segment representing a particular directory, and repeat the analysis for that directory,2 right click that segment to open a file manager or terminal emulator in that location, or copy to clipboard or delete the directory, and they may right click the segment representing a file to open it, copy it to the clipboard, or delete it.
JDiskReport is a nice tool, it requires Java 6 or later, Java 7 is recommended.
There is a fully rewritten version of KDirStat, by the same author, named QDirStat. Fast, customizable, using Qt5, desktop-agnostic (not depending on KDE components), and showing a squared view rather than concentric circles, which I personally find clearer. There is a ppa available for the installation.