As indicated, onmouseout is the opposite of onmouseover (note the capitalisation). However if this is for doing things like rollover effects on buttons then the CSS :hover pseudoclass may be preferable.
This is a somewhat grey area - you can do it via either method and the advocates of each would recommend their way - but it all depends on just what you want to happen when the mouse is moved on and off the element.
The big downside to the CSS method is that IE6 doesn't support :hover on anything but <a> elements - IE7 will only do so if your DOCTYPE is strict rather than transitional. The downside to Javascript is that the effect disappears if Javascript is turned off.