I'd say PDF. If it's OK that people can't edit it this is the way to go.
I think that still many people will have difficulty to use Open Document Format documents.
Theoretically they could just download Open Office but that's not something you would demand from your HR person;-)
Rich Text Format is an option if the addressee wants to edit the document.
For the resume:
I have mine in PDF, I made sure that
- it is less than 5 MB including references
- the meta data is OK
- it is searchable (not necessary, but I like
- it looks good when I print it on my B/W printer
Plain text (*.txt) has been mentioned by many others.
If you want to communicate only prose this is probably the best thing to do.
If formating is important (like for a resume you send to HR) or you must include
images, tables, equations, etc then I'd recommend PDF.