PhotoRank
You can increase a photo's popularity by moving your mouse over it and clicking the thumbs-up symbol that appears. You can cast one vote per photo. 
You can also rate a photo or gallery with stars when you leave a comment.
There are other factors...like time. Photos from events past will usually be less popular than recent ones.
How do I find the most popular photos of Rome?
Simple! Go to SmugMug's browse page, then enter Rome in the search box. You'll see a box: SmugMug keywords matching 'Rome'. Click the word Rome listed in that box.
You'll be taken to the first page of 47,000 (whew!) Rome photos. Notice in the top left of the page there's a link that says most popular. Click it and lose yourself in dreams of Rome.
Context-aware search
The search box, which is atop most pages, searches help pages when you're on a help page, all of SmugMug when you're on SmugMug's homepage, your SmugMug site when you're on your homepage, and the gallery you're viewing when you're viewing a gallery.
Both browse and search are made vastly more powerful and convenient for you and your admirers if you use keywords.
What? You don't want thumbs?
All subscribers can disable PhotoRank thumbs on a per-gallery basis in your gallery settings.
If you're a Power or Professional subscriber, you can suppress the PhotoRank thumbs for your entire SmugMug site by adding the following code to the Javascript Footer section of your site customization page:
displaySmugPopular = false;
By default, your own most popular photos appear in their own section of your SmugMug homepage, but when you're logged in you will see a link to hide that section.
Have thumbs but no popular photos?
Keep in mind that:
- Photos from unlisted and/or password-protected galleries will not show up in popular photos on your homepage or on SmugMug's pages.
- Hidden photos will only show up in your popular photos section when you're logged in as account owner.
- If your Site Visibility search settings are "No" in your Account Settings, or "No" for in your gallery settings for a gallery, those photos will not be included in popular photos.
- Anytime you Replace a photo, it starts over with a clean slate and no popularity.