Update December 2012:
The list below is obsolete, as WP changed many of the themes. To make their appearance more uniform, they say…
In the majority of themes, posts on category or other archive pages show up just as they do on the main posts page. But in some themes only the beginnings of posts are shown, and in a few themes you only get titles or thumbnails.
[But see note 3]
Autofocus [if post includes image]
As on main page
[All the rest]
Things to note:
2. The number of posts per page is set in Settings > Reading. Currently that setting applies to all post pages: you cannot set a certain number for the main page and a different number for category or archive pages.
3. When only the beginnings of posts are displayed, all html tags are stripped out. This means that italics etc. will show as plain text, links will also show as plain text and won’t be active, and images etc. won’t show up at all in those beginnings. In some themes you can override that by using the Excerpt function. The themes listed in the second column of my post on Excerpts can be made to display full posts in category/archive pages if you copy the whole content of each post from the html editor and paste it in the Excerpt box (except if the content includes shortcode objects). They can also be made to display titles only, if you use a no-content excerpt (i.e. write nothing but a space in the Excerpt box).