How to make a text box have rounded corners?

You could use CSS to do that, but it wouldn't be supported in IE8-. You can use some site like http://borderradius.com to come up with actual CSS you'd use, which would look something like this (again, depending on how many browsers you're trying to support):

-webkit-border-radius: 5px;
-moz-border-radius: 5px;
border-radius: 5px;

This can be done with CSS3:

<input type="text" />

input
{
  -moz-border-radius: 15px;
 border-radius: 15px;
    border:solid 1px black;
    padding:5px;
}

http://jsfiddle.net/UbSkn/1/

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However, an alternative would be to put the input inside a div with a rounded background, and no border on the input