How to make a texture that tiles with no visible join
Paint by Zaweba makes tiling textures with a distort filter that joins the edges, Wrap-Around Mode for painting across them and a 3 x 3 Pattern Preview.

A good tiling texture needs three things, and Paint by Zaweba has a tool for each. A filter in Filter > Distort shifts and blends the picture so its edges meet. View > Wrap-Around Mode lets you paint, clone and filter across the edges as if they weren't there. And Pattern Preview shows the picture repeated 3 x 3, so you can see the repeat as it will really look.
Textures for games, 3D models, fabric prints and website backgrounds all need to repeat without a visible line where one copy meets the next. The join is the easy part. The harder part is avoiding obvious repeats, where a distinctive mark shows up in the same place every tile.
What you need
A source picture with fairly even lighting and texture, such as a photo of gravel, bark, fabric or plaster taken straight on in soft light, and Paint by Zaweba on Windows. Strong shadows or a gradient of light across the photo will show as a pattern when it tiles, so even it out first if needed.
Step by step
Crop the photo to a square, or to the size your texture needs. Many game and 3D tools like sizes such as 512 or 1024 pixels.
Run the tiling filter from Filter > Distort. It works on the edges so that the right side carries on into the left and the top into the bottom. You now have a tile that meets itself, though there may be some blurring or a visible cross where the work was done.
Turn on View > Wrap-Around Mode. It has no shortcut by default, so assign one if you use it often. The artboard is shown 3 x 3, and anything you do near an edge wraps across to the opposite side: brush strokes, smudging, the clone stamp, the bucket, filters and even live filter layers. Use the clone stamp and healing tools to paint out any visible cross or soft areas. Because your strokes wrap, you can work right across the join.
Use Pattern Preview to check the result. It tiles the picture 3 x 3, and edits show in every copy as you make them, so you can spot patterns that only appear when the tile repeats.
Breaking up repeats
Look at the preview from a distance, or zoom out. Your eye will find anything that stands out, a dark stone or a bright speck, repeating in a grid. Clone over those features or tone them down so the texture reads as an even surface. The goal is a tile where nothing catches the eye.
Uneven lighting shows up here too. If one corner of the tile is darker, the preview will show a soft checkerboard. An adjustment layer through a soft mask can even it out.
Getting a good result
Wrap-Around Mode works on documents with a single artboard, so keep the texture in a document of its own. Save the finished tile as a lossless format such as PNG, since compression artefacts become visible when they repeat dozens of times.
For painted textures rather than photos, start with Wrap-Around Mode on from the first stroke. You never have to fix a join you never made.
Other uses
The same tools make fabric repeats, wallpaper style backgrounds and patterns for the Pattern Stamp or pattern fills. Whatever the use, the routine stays the same: make the edges meet, paint across them, then check the repeat.