Similar to what already exists regarding web banner sizes, is it possible to find the list of most commonly used picture/image/icon sizes on the web (e.g. 16x16 for small icons, 24x24 for medium icons, 50x50 to 70x50 for small profile pictures...)?
There is no standard as icons can be of any size depending on how they're going to be used. The most common sizes I've seen based on icon sets I have downloaded are:
Do you see a pattern here?
There are no default image sizes for websites as a whole. Dimensions are dictated by how the website needs to use them. When size does matter is when you are using a third party service and have to conform to their standards. Examples would be gravatar sizes. But if someone wanted to use different sizes for their own blog engine they could certainly do so and wouldn't break anything or cause confusion elsewhere.
So use whatever sizes you need to use and only worry about what someone else is doing when you have to interface with their API or any form of interface that has size requirements.