If you're developing an ASP.NET application, adding a rounded corners extender to your panel is the most common way to get rid of the pointy ends. You can add borders to the rounded panel as well as assign a different color to the top and bottom edges of the panel. You'll probably run into the issue of not being able to add padding to the panel as that makes it go haywire. A work-around is to create another panel or div within your rounded panel and add padding or margins to it.
Here are some samples with both that I came up with:
The Rounded Corners Extender can have borders and edge colors applied to it.
Adding padding to the Rounded Corners Extender keeps it from resizing with the window and makes it protrude from the right.