desktop-globals-to-save is a variable defined in `desktop.el'.
Its value is

(desktop-missing-file-warning tags-file-name tags-table-list search-ring regexp-search-ring register-alist file-name-history)

List of global variables saved by `desktop-save'.
An element may be variable name (a symbol) or a cons cell of the form
(VAR . MAX-SIZE), which means to truncate VAR's value to at most
MAX-SIZE elements (if the value is a list) before saving the value.
Feature: Saving `kill-ring' implies saving `kill-ring-yank-pointer'.

You can customize this variable.