As analog as tabletop games are, designing them is easier with software; heck, a lot of things are easier with software! From conceptualization to final art, here are the programs I use and for what, as well as some alternative programs:
This is the primary program I use to write rule books. InDesign makes it easy to put images and text together in a visually appealing way and you can size it to your cards/box! Exporting to PDF is simple so the file is good to go printing-wise. InDesign isn't just for rule books either! You can use it to sort cards for printing and it's a great alternative to PowerPoint if you need to make a presentation!
The cons? This is a design program so there's a bit of a learning curve for anyone unfamiliar with it; and it's Adobe so it's a bit expensive.
Alternatives: If you can't get your hands on InDesign, there are always alternatives to every program out there. Although I've never used it myself, I've heard of people using Scribus to great success. Of course, if you only need a program to write down rules, there's always the good ol' Microsoft Office suite and OpenOffice if you need a free alternative to that.
I use Excel for a lot of things but in game design, I use it to organize cards, pieces, quantities of each, each of their effects, and so on. This program is essential for me to keep things organized as I mess with card quantities and change cards and pieces. Sometimes, I will use this program lay out the early prototypes for testing before I have art (or even an inkling of what will work or not). I highly recommend using Excel or something like it when designing a game - or anything with a lot of pieces - where it's essential to keep an organized file.
Alternatives: Microsoft Excel isn't the only row-and-column program that can keep you organized. There are some great free alternatives, and yes, I've used and may still use the alternatives I'm about to suggest. OpenOffice Calc is an Excel clone which is excellent. If all else, fails, Google has a Excel clone too! Take a look at Google Sheets. If you're working with other people on your game, it's essential they know all the numbers and changes you make and Google Sheets really makes it easy to share.
Adobe Illustrator is the standard for vector graphics. Logos, graphic design, art if you like that vector style - all of that can be done on Illustrator! The beauty of Illustrator is that you can import Illustrator files to Photoshop if needed.
Alternatives: Illustrator is a robust program with a lot of features. Any vector program can do the essential things that Illustrator does but may not have all of the same features. I've never used this program myself but Inkscape is a popular alternative that many game designers use. Another cheap alternative is Affinity Designer, which is mostly like Illustrator with some Photoshop features. Affinity Designer files cannot be exported to Illustrator but can be exported to Photoshop.
Just about everyone and their dog knows about Photoshop. This is a great tool for art! You can draw just about anything and its list of features is long! If you need to mess with some photographs or draw some card or box art, this is the program you'll want to use.
Alternatives: Gimp is probably the go-to alternative to Photoshop. The important features we love in Photoshop are all there and, best of all, it's free! Another alternative if you're looking for another painting program is Sketchbook Pro. It's great for sketching but the downside is that it's just like drawing on paper...except digitally.This minimalist program shines with the drafting tools and symmetry feature you can use. If you're just starting on digital painting, Sketchbook is a great gateway program.
NOTE: None of the programs I've mentioned are sponsoring me in any way (if you work for any of these and you want to give me money, feel free). These really are the programs I use and I have used many of the alternatives suggested as well.