How to customize the mode line ?

[Apokrif]

I'd like to add a simple message to my mode line. Of course, I can
type for instance:

(setq mode-name (concat mode-name "foo-bar"))

but as mode-name is a variable and not a function, this works only for
the current buffer. How can I modify this line so that the message
keeps being displayed in all buffers when I stay in a particular mode
(and change the message from time to time )?

-- 
Signature spirituelle.