For everyone who is using version 6.4.x of Events Calendar and have been having trouble with the Previous/Next links at the bottom of the sidebar widget, I have came across the solution, at least for my WP install.
Under Options, just enter the number "1" (no quotes) in the <b>Length of day names in Widget Calendar</b>. That will generate both the Previous/Next link at the bottom and the "S M T W T F S" day labels at the top of the calendar.
The problem was that the Length field is empty (giving a value of 0) by default.
Let me know if this works for your site as well.