Client’s specs include displaying Today’s Events and Upcoming Events in the sidebar, in separate Widgets. Let the Event Calendar WordPress Plugins search begin.

Currently using WordPress 3.5.2.

The Events Calendar (v 3.0)
Widget: Upcoming events
Note: this only shows Upcoming events, NOT Today’s events
Compatible up to: 3.6
Last Updated: 2013-7-2
Downloads: 438,550
4 out of 5 stars (202 5-stars)

Calendar (v 1.3.3)
Sidebar function/Widget to show todays events
Sidebar function/Widget to show upcoming events
Compatible up to: 3.5.2
Last Updated: 2013-4-28
Downloads: 409,954
3.9 out of 5 stars (61 5-stars)

All-in-One Event Calendar (v 1.9)
Upcoming Events Widget
Compatible up to: 3.4.2
Last Updated: 2013-2-5
Downloads: 404,624
4.2 out of 5 stars (303 5-stars)

My Calendar (v 2.2.5)
Widget to show today’s events
Widget to show upcoming or past events
Compatible up to: 3.6 beta
Last Updated: 2013-5-25
Downloads: 277,266
4.3 out of 5 stars (68 5-stars)

WP Calendar (v 1.5.3)
Widget
Compatible up to: 3.5.2
Last Updated: 2013-1-7
Downloads: 83,188
3.9 out of 5 stars (19 5-stars)