As mentioned in the registers entry, many programs only allow you to paste the last copied/cut text block, and that is what the kill-ring does by default (when you press C-y). However, you can choose older ones using the menu (Edit/Paste from kill menu). Alternatively, you can use a prefix key (e.g., M-3 C-y will insert the third most recently killed ('cut') text).
The kill 'ring' behaves mostly like a list; by default (emacs 22, 23) there are 60 positions available in the ring, after which older entries are thrown away. You can put (setq kill-ring-max 120) in your .emacs in the unlikely case that 60 is not enough.
Update:An anonymous commenter mentions the useful M-y ('yank-pop') key binding, which lets you cycle through the items in the kill-ring. Quite useful indeed, thanks!
If you're using the GTK+-version of emacs (the graphical version in X/Linux/Unix environments), you can even have the Edit/Paste from kill menu-menu in a separate frame (window), and paste text by clicking there. To this, go to the menu Edit/Paste from kill menu, and click on the dotted line at the top of the sub menu.