I enjoy developing my own software, but there are many applications that I use for various projects.
TinkerCAD - Used for: 3D printing. This is a great starting point for 3D modeling, but can be a bit limited for more advanced applications. I used this a lot in the STEAMlab at the Children's Museum of Bozeman when teaching kids how to design objects in 3D and then 3D print them.
Blender - Used for: 3D printing. Open source 3D modeling and animation software. You can 3D model, animate, render and composite in this all in one package. It's not designed with 3D printing in mind, but it can certainly be used for it. It's a bit advanced for someone just starting out with 3D printing, but it can do a lot.
Fusion 360 - Used for: 3D printing, CNC, laser cutting. Fully featured CAD software that can be used for 3D design and manufacturing. Integrated CAM makes it great for CNC milling. It's the only affordable application with 5-axis machining capabilities. It's free for hobbyists and startups making less than $100,000 a year, which makes it a great option.
Meshlab - Used for: 3D printing. I don't use this often, but mostly because I haven't taken the time to learn many of its features. It can be a great tool for fixing 3D models by converting to volumetric representations and back to a mesh (though, I usually prefer to just use my own command-line tool called stl_boolean, but getting it up and running isn't for the faint of heart). I've also used it for support generation for my B9Creator.
Netfabb - Used for: 3D printing. Netfabb is great for checking your 3D model for errors such as non-manifold edges and holes as well as taking measurements to check thicknesses, radii and more.
Inkscape - Used for: Laser cutting. Open source vector drawing application. It's designed for general vector graphic design rather than CAD applications, but its free and widely used. Almost all my laser cutting projects use Inkscape, but because of its focus as more of an artistic tool it can be tricky to be precise.
Eagle - Used for: PCB design. I use Eagle for all my circuit board designs. There's a free version that can design small circuit boards, which is great for hobbyists and can be upgraded for more serious PCB design. Many PCB manufactures accept EAGLE board files, but it can also export to other formats.