Quick and Easy rivers in Inkscape with Fractalize and Tweak
This tutorial assumes basic familiarity with Inkscape including the Bezier and Edit Paths tools.
First, Ctrl+Shift+D to bring up the Document Properties. Select "Snap", and make sure Nodes are snapping to Nodes.
Now select the Bezier Tool and draw the rough path of your river as a sequence of straight segments roughly the same length.
Next add major tributaries the same way. Start at the corners of existing paths. The line will snap to the corner automatically.
Select the paths and choose Effects → Modify Path → Fractalize. Turn on Live Preview, set subdivisions to 1, and pick a smoothness that look good. Apply when you are done.
Use the bezier tool to add lesser tributaries using the new segment length. Make adjustments to the paths with the Edit Paths tool as you see fit.
Adobe Illustrator conversion
To accomplish this task in Adobe Illustrator, use Effect > Distort & Transform > Roughen. Set the Points to "Smooth" and adjust the Size and Detail downward.
Convert the stroke to outlines with Object > Path > Outline Stroke, then use the Bloat and Pucker tools (hidden under the Warp tool) to adjust the stroke width. To adjust the properties of the tools, select the tool, then double-click on its icon in the toolbar. Or you can hold down alt to interactively change the brush size prior to using it.