In Microsoft Word, it is common to create a floating text box, separate from the normal body text, that can be placed anywhere on the page. The body text will then wrap around this text box so everything is readable.
In (La)TeX, the wrapfigure package allows figures to be created that the body text will wrap around, but they may only be placed at the beginning of paragraphs and on the edges of the page. The package doesn't seem to allow absolute placement independent of the body text and margins. Using the absolute-placement package textpos in conjunction with wrapfig will simply break the wrapping.
So how can I have the best of both worlds—text wrapping and absolute placement (at the very least, vertical placement)?
Something like the diagram in this question, or this image from Word.
(Edited for generality and clarity.)