I know that you can use Alt+F2 for this, but using super is much more ingrained for me since I've seen Windows Vista (I am using Linux at home and Windows systems at work)
Brisk Menu. It binds to the Windows key by default and still somehow allows shortcuts like Win+R to work.
The windows key is a modifier like shift, alt or ctrl and hence at first it seems like a really, really bad idea to use it a shortcut by itself. The above programs hence implement the same behind-the-scences workarounds other desktop environments and windows use: treat pressing and releasing win alone as special.
You can of course also use this for other keys, for example
caps alone-> Esc
caps+c -> ctrl+c
Alternatively, I win+space instead of just win also is quite natural shortcut.
For me it became the most important feature of a window manager / desktop.
That's how Unity (Ubuntu's default DE) worked, until they transitioned to GNOME.
I'm not familiar with recent Windos but pressing the "Super" key on Gnome opens the "overview" screen (or what's called) with a big "Type to search..." text box that can be used to search files to open or programs to launch.
P.S. I prefer to use shortcuts to launch the common programs, using an extension that mimics Ubuntu Unity style Super + number_key, according to the order in the "Favorites".
The "problem" with Mate is that it just works. I interact with Windows and OSX daily, and I have yet to find a feature that makes me thing "I wish my desktop environment could do this". Mate gets out of my way and lets me work.
In other words, it's boring. There's nothing new and shiny to be excited about, because it's as good as it gets. I left Gnome 3 because I was tired of visual effects getting on my way, but those visual effects were what attracted me to Gnome 3 to begin with. I think Mate lacks that "wow!" factor and, as grateful as I am for that, I think this might stop it from being more popular.