Pencil & Paper- old school I know but you can't really go wrong and its the basis of everything I do- Good for keeping your skill set polished and always handy, just in case.
Art Rage: My personal weapon of choice, quick, simple and because I tend to use real materials I find it easier to use than some others.
Photoshop: This is the favorite for many CG artists, great for image manipulation, and good to use and get to grips with. Also its used extensively within industry.
Coral Painter: This is another good realist material program, much like Photoshop but more in depth than Art Rage.
Adobe Sketch: Not too dissimilar from Art Rage, very fluid, up to personal choice on this one.
MS Paint: Yes even paint!
Toon Boom: Although this is a 2D animation program, its still good for producing vetor based pictures and quite quick to get to grips with.
Illustrator: A more in-depth vector based program, used extensively with in the graphic design industry and as its name suggests for illustrations!
2D Animation Programs:
Toon Boom: This is a nifty little program, and can produce some great results.
Adobe Flash & Macromedia Flash: This is a good staple program to know especially when doing 2D animation work.
Photoshop: Yes you can animate in the newer versions of Photoshop, not as specialized or as in-depth but is good for animatics or other fundamental work.
3D Animation & Modeling:
Maya: Industry standard, a good all rounder and can be as simple or as in-depth as you want to get into it- if your just starting with this program start slow and work your way up.
3D Studio Max: This is the standard for the games industry, another good all rounders, I started to learn on this program, if you can use max you can use maya and visa versa, its just a case of learning a new language to what all the functions are called.
Blender: i have never had to use this program so I can't really say much, but I have seen some awesome animations produced from it!
Lightwave: again another program I haven't used, so it would be unfair to comment on!
Cinema 4D: Not much experience, but looks cool!
Zbrush: I have a crush on this program, much to my GF amusement. Its great, small and robust its a 2.5D program but it doesn't feel like it. I find that i can do almost everything in it and will often just sculpt to relax for fun rather than doing anything serious.
Mudbox: this is a good sculpting program, I have had a few good results from it.
Sculptris: Simple and easy to use, no worries over polygons, fun to play in, but likes the dreaded triangles so be careful if using it for animation purposes.
Maya: It has a soft selection mode that kind of simulates sculpting, its good for re-topologizing and creating a good edge flow for lower poly meshes.
Any 3D program should have a UV mapping function, some can be quite complicated or awkward to use, but you might find that you dip in and out of these programs to achieve the effect that you want.
3D Coat: I have used this program, and its very practical.
Road Kill: Again another useful program, similar to 3D coat.
ZBrush UV Master Plugin: This is possibly the most useful plugin for zbrush if nothing else. I tend to use this, cutting my borders in maya, then un-wrapping in zbrush, stitching any misc stuff in maya, then back to zbrush for a base paint before going into photoshop...simple!
Topogun: I haven't used this program much as i find it easier to to work with my low meshes to start with, and do things the old fashioned way.
3D Coat: I haven't used the re-topology function in this program so.....
Windows Movie Maker: quick simple, not much else to say!
Premiere & Pro: This is a good program for learning the foundations, and most of the adobe products have a similar UI system so it makes it easier to cross programs.
Final Cut Pro: This is industry standard and a good program, not too dissimilar from Premiere.
I find that most compositng programs are very similar, so rather than going through each one, here's a list. I have never really used any one of them for very long or had to switch from one to another, so after a while they all merge into one program in my head!