How do I export map images of larger areas?

• Export tab: This is probably the easiest solution but only works for small areas. Select one of the options that is suitable: Raw OpenStreetMap XML Data, Mapnik Image, Osmarender Image, Embeddable HTML
• Maposmatic: Is a service that lets you create pretty city maps in any size in pdf and svg format. They also come with a street index.
• bigmap.cgi: This lets you select an area and download a small perl script that, when run, outputs the requested area in one big .png file. It stitches the grphic together from the single 256x256 pixel tile images.
• Walking papers: Lets you easily select an area and print the map on a A4 (or letter) page. This is incredibly handy if you need a city map when exploring a new city, or to print a map and (with a real pen!) want to make notes, additions and corrections before fixing the map. Walking papers also offers a cool scan service where you can upload those annotated maps.
• Maperitive: Desktopp app, written in mono, can produce both bitmaps, SVGs and web tiles from OSM XML files.

Render on your own. Only do if you know what you are doing and need e.g. to customize your maps.

• osmarender: http://wiki.openstreetmap.org/wiki/Osmarender
• or/p: is an osmarender drop-in replacement that is faster (written in perl). See http://wiki.openstreetmap.org/wiki/Orp
• mapnik: Full blown mapnik install is probably NOT what you want to do when all you need is some nice maps. But hey, here is information about the mapnik renderer.

If you decide you want to customize or render things on your own, also have a look at the related question "How do I render Maps for my own website".