Don't have Photoshop? No problem! Free drawing software lacked features and compatibility drawing hardware a decade ago. However, the evolution of free drawing programs today are extremely good that it's comparable to paid software. Here's what to look for.
First of all, a drawing program will need to provide the following features: proper pressure sensitivity or hardware support, adequate assortment of brushes, layer management, color correction tools, and filters.
Out of all these features, hardware support is key to qualifying an excellent software. This is because movement control, pressure sensitivity, tilt, and other stylus functions are what is going to make or break the software's popularity or usage.
The ones I am going to go over is GIMP, Inkscape, MyPaint, and Corel Painter (this one is a special case as it could be considered free due to being given out with WACOM tablets in their software bundle). With the exception of Corel Painter, all of these are free to download and use permanently.
GIMP came about the need to emulate the extremely costly, but popular, Photoshop software. GIMP is a well rounded software that has a lot of drawing tools, filters, layer management, color correction tools, and most importantly, hardware support.
For the purposes of drawing, there are few differences to its original expensive counterpart. If there is a personal criticism of this software, it would be its weak vector support. Aside from that, this is an excellent software to draw with.
Since the software is free with a huge community backing, there will always be large number plug-ins and packages you can get on the Internet. For example, there are a lot of brush packs you can import. Just search around.In terms of out of the box usability, it just means you may or may not have everything you need initially. Therefore, you may require a bit of time setting up the plug-ins and brushes you need to start drawing or any other artistic ventures.
If GIMP is the king of free raster images, then Inkscape would be the king of free vector images. Unlike raster images, each sketch line and block of color of vector images are mathematically created.
This means that you are no longer limited to a pixel canvas dimension for quality. Instead, the quality remains the same regardless of how small or large the image outputted. For commercial purposes, vector images are preferred over everything else.
Stuff that you can do with vectors can include cartoons, logos, technical drawings, and general graphical advertisements. The downside is that it takes far more time to create and may not be useful for free hand drawing in general.
This is why GIMP and Inkscape go hand in hand. Both software can import files to one another to improve the efficiency of any work flow. It's a great piece of free drawing software once you understand the importance of vector images.
Compared to the other two, MyPaint is relatively new. If GIMP is a well-rounded raster editing/drawing software and Inkscape is a vector expert, then MyPaint would be a software specializing in emulating traditional drawing and painting media.
Where it lacks features in filters and general post image processing, it makes up with its ability to draw and paint on your computer with greater ease as the majority of the options available are through utilizing and making new brushes.
Even if you don't have a brush that you like, you can always download packages online. Despite being new, there is enough user generated knowledge to answer any questions as well as drawing kits available that you can get to further enhance the software.
As it's new, the software will be always changing with new features being added all the time. In other words, it may not be up to par with your work flow just yet until a few more feature are introduced in months or years later.
If GIMP is related to Photoshop, then MyPaint would be close to emulating Corel Painter. That means it is a very capable raster painting program that is far more feature rich than the equivalent free counterpart.
Normally, this is a paid software. However, as far as I can remember, Corel Painter is usually bundled with WACOM Intuos (or higher) tablets in their graphics suite. So by purchasing tablets from this brand, you will have a license to one of the best drawing software out there automatically.
It is also this mutual packaging that has led Painter to be used extensively by professionals and be the default choice for digital painting everywhere. As a result, there are a lot of resources on this 'free' drawing software.
Furthermore, the graphics suit included with the purchase will include Photoshop Elements, which is another good image editing software that you can try to draw with. There may be other software bundled with it as well, but it will be dependent on region.
Since the bundles change over time, it is difficult to say what will be included in the purchase. From a practical standpoint, it is a good deal and will allow you start drawing immediately.
There is another possible free drawing software that I would like to mention: Paint.net. However, as it doesn't have pressure sensitivity support at all, I do not recommend it. Just stick with these suggestions for now until the developers update it accordingly if you want to try out other drawing software.