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In ArcMap, open the data frame property page (right click in the map, or "Layers" in the table of contents). Select the Coordinate System tab. Browse or search (in 10.1) for the projected coordinate system you want to use. Once you okay the selection, it will be set as the data frame/map's coordinate system. Any layers that are in a different coordinate system will be projected on-the-fly to that coordinate system.
Thanks for reply but my problem is after selecting a projected cordinate system like UTM which zone must be selected? as I already mentioned I am creating world wide map.
Ah, I misunderstood. You can't use UTM for a worldwide map. A UTM zone was designed to support 6 degrees of longitude (with a little extra on each side). It's possible to display more, and we allow almost up to 90 degrees wide, but the distortion due to the map projection, transverse Mercator, is considerable. It's just not a good choice for a worldwide map. For display, something like Winkel Tripel (used by National Geographic) or Robinson (used to be used by National Geographic) are better choices.
An 'interrupted' map projection could be Goode Homolosine which comes in land and ocean versions.
All of these are in the World folder under projected coordinate systems.