To add custom application icons to your projects, or a favicon to your websites, you will need ICO icons. To make one you can export an image as an ICO (.ico file format), convert an existing graphic to the file format, or download a premade one.
"ICO files contain one or more small images at multiple sizes and color depths, such that they may be scaled appropriately. In Windows, all executables that display an icon to the user, on the desktop, in the Start Menu, or in Windows Explorer, must carry the icon in ICO format." (Wikipedia)
Creating ICO Icons
You can export directly from an application like GNU Image Manipulation Program without having to add plugins. GNU Image Manipulation Program (GIMP) is an open source image editor like Photoshop. It is powerful and a great option for graphics.
Show Screenshot
Other graphics software might need a plugin. Photoshop CS6, for example, needed a plugin to export as .ico. There are several free ones available, though, so if you are open to adding a plugin it is an easy fix.
Converting Images to ICO
You can also use an online converter. Upload your image, and then download the file as an ICO. As with plugins, there are many options to choose from on the web.
There are also sites that allow you to create an ICO icon in your browser. Many of these are grids that allow you to color squares that represent pixels. You won't be able to get the same range of color, shapes and effects as if you used a graphics program, but they are great for simple designs, or 8-bit retro styles.
Some, like favicon.cc, have previews of what the icon will look like at smaller sizes. The above screenshot shows a preview of the result as a favicon in a browser address bar.
Premade ICOs
There are a lot of premade ICO icons you can download. Here at Programming Is Fun there are nine .ico format icons that you can use, share, and/or adapt (even for commercial use) as long as you credit the source (Creative Commons Attribution-ShareAlike 4.0 International License).
There are also several sites that host icons, many of which are public-domain. Be sure to look at the license before you use any media in your project, though. Sometimes they are free to use, but not free to modify, share, or distribute.