Marissa Mayer? Nobody knows at this point, but she's sure to focus on the brand and user experience, her strengths while at Google.
The Yahoo! home page has definitely evolved over the years, and it's clearly not Google-like. Above, what the top of the home page looked like in 1996 (according to the Internet Archive's Wayback Machine), just two years after it was founded. Remember, Google was just getting started at this point, but its search page was stripped-down from the start.
By 2000, Yahoo's home page was more crowded and shopping was clearly being promoted, as you can see from this screen capture at left (again, thanks to the Wayback Machine). The Yahoo! logo remained red...
Now, in 2012, Yahoo shows trending topics at top right, some news in center, other Yahoo sites along left column, and "most popular" at mid-right. Note that the Yahoo! logo is purple, not red.
10 million Facebook likes. It just has to decide what the brand will stand for. What will its home page look like in 2013?