You can avoid Upcoming Event List Widget scroll bar by carefully setting your list height and by limiting the number of events you display in the Upcoming Events List. For exampe, set an Upcoming Event List height of 400px with only a max of 5 or 6 events displayed will not show a scrollbar.
Go to Admin Menu -> Web Wigets -> Upcoming Event List -> Event Tab ->
Under "Max Events" insert 5 or 6 as the maximum -> SAVE
Next, Go to List Tab -> Set "List Height" to 400px approximately -> SAVE
Note: these are just example values to get you started. Adjust the list height and max events values as needed to accomodate your webpage and event decription lengths. You can adjust the number of characters displayed in an event description under the "Events Tab."
Some customers opt to make the upcoming events list appear to blend into a webpage. Some suggestions for doing this would be to set the List Tab "Background Color" to match the background of the webpage. Also, you can remove the the event list heading by checking the "Do not show heading" checkbox -> SAVE
Here is a customer example of the upcoming events list without a scrollbar: