Post Formats are merely a way to indicate to the theme how a post should be styled. So, ultimately, it’s up to you.
But I know how useless “it’s up to you” can be … so let me give you a couple of examples:
WPCandy
If you are knew to the WordPress community, you should start reading this site. It’s a fantastic resource.
The best example from this site is how they handle the “link” post format. Links get their own icon in the UI (to designate them as links), a short description, and a title. The title links to the remote link rather than to a permalink for the site.
Tapestry by StudioPress
This is a child theme for Genesis that implements post formats by default. Different post formats have different layouts in the theme – photos, galleries, and quotes lack titles, for example.
Unlike WPCandy, though, link post formats lack titles. Their links (when you click the link icon next to a post) take you to the post permalink where you then click through again to get to the remote content.
So Really …
It’s entirely up to you. The goal of post formats isn’t to tell you how to style your content or dictate design decisions, it’s meant to provide a standard context to post content.
If I draft a post that’s a link out to another site, I mark it as a “link.” My current theme, though, doesn’t do anything fancy for post formats.
But if/when I change themes, that post formats stays around and if the new theme supports post formats, then my link post is styled a bit differently.
When it comes to links, though, my personal recommendation is to go the WPCandy route. Make the title link out to the remote content. And if there’s no author-provided title, use the link’s title. From a user perspective, this then involves fewer clicks to get to the content I really want to see.
But I guarantee others in the community will disagree with that use case. So when I say “it’s up to you,” all I can offer is a personal opinion.