Typically I put a lot of the common code in the MasterPage. I use partial views for larger, self-contained units of functionality. For example, a grid that gets reused across many but not all pages or the header login "controls." Sometimes it's a combination of the two. For example, my main, unauthenticated menu items appear in the MasterPage mark up, but I use a partial view for my authenticated menu items which contains the logic for dealing with which items show depending on the user's role.
The other thing that you might want to think about for small HTML snippets is HtmlHelper extensions. I find that this is a good way to set up particular kinds of HTML elements. For example, I have an extension that will add a "button" that will work with either javascript enabled (renders as an anchor) or disabled (renders a button inside a noscript tag). This sort of thing is better as an extension, in my mind anyway, than a partial view since it's not really a "view" of anything.