Among the major word processors that support Unicode and the bidirectional algorithm are OpenOffice.org Writer (1.01 or higher), a free open source word processor with freely available spell checking dictionaries in multiple languages including Hebrew, and Word (97 or higher in non-Hebrew versions), generally bundled in new PCs. They use a publicly available XML file format called OpenDocument and a series of proprietary binary file formats respectively.
Both of them can read documents containing Hebrew characters "out of the box" without changing their configuration and/or adding anything as long as appropriate fonts for Hebrew characters are installed. If you want to compose your own documents in Hebrew characters, you have to change their configuration. In order to enable Hebrew in OpenOffice.org Writer, 1) go from its toolbar to "Options" -> "Language Settings" -> "Languages", and 2) check "Enabled" for "Complex text layout (CTL) language". Then two icons indicating left-to-right and right-to-left paragraph directions will appear on the toolbar of OpenOffice.org Writer. In order to enable Hebrew in Word, 1) go from the toolbar of Windows to "Programs" -> "Office Language Settings", and 2) choose "Hebrew" from "Available languages" and add it to "Enabled languages". Then two icons indicating left-to-right and right-to-left paragraph directions will appear on the toolbar of Word.
Although Word is widely used among scholars of Jewish languages, too, it may not always be a wise decision for various reasons to use Word format to send your documents to your colleagues without making sure that they also have Word and/or want to receive your writings in this format. This is also the case with OpenDocument, though for a different reason (it is not so widely used yet). Safer, more platform- and device-independent document formats would be 1) plain text, 2) HTML/XHTML (with CSS) and 3) PDF. Incidentally, OpenOffice.org Writer can not only open Word documents but also save its own documents in Word and PDF formats. Its file size is generally several times as small as that of Word.