I'm not very original, so I stick to:
Github, to upload code I want to share, search for things I need and whatnot
Collab, to program and share commented snippets with students and colleagues
TeXShop: Latex rulz. At least, whenever it's not driving you mad. If you don't work on a Mac, WinEdt may work for you. And you can go cloud-y with Overleaf, too.
Open Office: for compatibility with the rest of the world, and this one is free!
Adobe Indesign: this is just the thing for page layout design, but it is not cheap. You can try instead Scribus, which is totally free, multiplatform and has the most important features. Both generate PDF documents suitable for on-line publishing in, e.g. Issuu.
If you are cowriting a paper, Sharelatex might be better for you than your usual desktop suite.
Mendeley helps to organize PDFs and references for your articles. It has online and desktop clients. You can add notes to the papers online and outline key paragraphs too.
Stormboard provides a simple tool to organize ideas and arrange them in the proper order. Good for cooperative work as well.
I'm kind of partial myself to Adobe Photoshop, but it you need something good and free, go for Gimp.
To switch video formats, I usually dig MPEG StreamClip in my Mac, but I was very fond of Virtualdub on PC. Take your pick.
If you are working on PC and need to play mov videos, I'd go for Quicktime Alternative. It works faster than Quicktime and mess less with the system.
For professional video edition, Da Vinci Resolve has a superb free version.
Dropbox: to keep your files synch-ed in all your computers
Dropbox Encore: to overcome the limitation of one accound/one Dropbox folder (for Mac only)
And there's always Google Drive or One Drive, obviously.