Depends on what I'm doing.
GIMP+imagemagick replaces Photoshop effectively for raster design (one for manual drawing, one for automation). For vectors, I use Inkscape. Tried Xara a little while ago, and almost switched to it but it couldn't open PDFs as I recall.
The only thing Adobe provides that I don't have an open alternative for is InDesign, and that would be a problem if I had any interest at all in editorial design. Granted, Scribus is out there, but it lacked a lot of functionality last time I tried it, so I doubt it would outright replace the adobe offering.
EDIT: I've also been meaning to try out synfig studio for something, but there doesn't seem to be much demand for animation hereabouts.
It runs on my choice of operating system (I use Solus).
I use Inkscape to prepare animations that I make in Synfig. Unlike Illustrator, Inkscape can save files as .sif.
I can quickly and easily install Inkscape on any other computer (for free) in case I'm away from my own workstation, or if I'm teaching somebody how to work with vector graphics.
I like that Inkscape's file type is (a version of) SVG:
I can open it with a text editor and understand it (to a certain extent). This is useful for web animation work.
I can also use git for version control with Inkscape files as they are text-based - I can't do this with illustrator.
I don't have to worry as much about obsolescence (eg. when Freehand stopped being supported and people couldn't open their old projects) - SVG is a web standard, and it's trivial for other programs to open it.
This is great, glad it works with sprite sheet rather than layers for separate frames. I've been looking into vector animation lately, and decided to give synfig a try today. Super impressed so far, it actually seems leagues ahead of flash in terms of flexibility, and it's open source. It's possible to export to animated svg also, though it might be a bit buggy for some things since it supports features svg does not.
Jashaka is pretty dead by now, isn't it?
Tbh there's no drop-in equivalent to AE, though blender can do a lot (if you know what you're doing). Natron's great for tracking etc, and for animating 2D vector elements there's Synfig.
Yes, I spent some time looking at that. Something like that might make a good foundation for a good game animation editor, but Synfig (IIRC) is primarily set up to create video, not Flash files that can be played back in real time. This year-old forum post is the top result on the site that seems to address the question -- no Flash exporting, but someone COULD implement it.
So the problem is there's no path from Synfig into my game other than raw video, but what I'm looking for is that 45k file that has a 15 second animation instead of the 400k of individual frames that I have to deal with otherwise.