I particularly like Cinnamon, it's very simple and nothing fancy (while still looking great and modern).
The other popular choices include:
Gnome
KDE (customizable to hell)
XFCE (very easy on resources, good for old hardware, or if you like simplistic DE)
LXDE (similar to XFCE in the resources department, but looks more modern, IMO)
There are others, but I can't speak for them as I've never tried them. I can't really describe modern Gnome as well, because the last version I used was 3 and it doesn't look at all as the same DE, so someone else will have to provide that info.