In Illustrator, you can make a swatch, give it a red color, and then color a bunch of things with it. Then, when you decide that you think blue would be better than red, you can adjust the swatch's color and everything turns blue. Is there an equivalent, either in Inkscape or some plugin, that can do something similar?
Yes, Inkscape does have swatches -- but they are a little tricky to figure out if you have never used them before.
In the Fill / Stroke Dialog, there is a fill type called "Swatches". Select the object that you want to apply a swatch too, then press the Swatches Fill/Stroke type to create a new swatch. This is also where you edit the color of an existing swatch. The same principle also works for gradients, but editing them works a little bit different, see below.
There is also the Swatches dialog (Edit > Swatches)that lets you see the swatches you have created, and set the swatch of a specific object. Note too that if you set the palette at the bottom to "auto", it will show all the swatches in a document.
Note that the colors in this gif look a little funky, but I hope you get the idea :)
To edit a gradient swatch, select an object with the gradient you would like to edit and use the gradient tool (Ctrl+F1) to edit it. Make sure that the option "link gradients to change all related gradients" (little lock symbol in the toolbar) is checked.