If you're only interested in saving the content of a document and don't need formatting, txt (documents) or csv (data spreadsheets) are simple but stable file formats.

If you want to preserve the format of a document, pdf is an acceptable standard. It's widely used and can be rendered by a variety of software and browsers. An archival version called pdf/a is optimized for stability.

The Microsoft Office formats docx (Word text) and xlsx (Excel spreadsheet) have been open specifications since 2007. If you have any files in the earlier proprietary formats doc or xls, which date from 1997–2003, you should update them by saving them as docx / xlsx.

Email

Consider focusing on certain threads or topics rather than saving your entire inbox. You can save individual email by copy-and-paste into plain txt or Print and Save>Convert-to-pdf.

Many email services have options to batch export or download in the mbox format or as a zip package. Look for this feature in your email service's Options, Account Info, FAQ, or Help sections.

For highest quality image files, the tiff format is preferred.

If using a digital camera, you may want to keep raw files as digital masters, although raw formats often require conversion to another format to be rendered.

For everyday use, jpeg is fine, although be aware that jpeg files lose quality through compression every time the image is saved, so you shouldn't use it for images you plan to edit.