The lrcat file is the catalog.
Before you move your photos and the catalog to a new computer, read this: http://www.lightroomqueen.com/2009/02/28/how-do-i-move-lightroom-to-a-new-computer/
PS: There have been some reports that Lr looses images when you move folders in Lr.
Therefore I would recommend that you choose the option of moving your image folders via your OS (Mac Finder / Win Explorer) and thereafter re-link Lr to the new location. Victoria Brampton covers both options in the link above.
Message was edited by: web-weaver: PS added
Sorry, I meant COLLECTIONS, not catalog.
And do you mean collections as in the Collections panel in Lightroom's Library, left hand side?
The collections are defined within the catalogue, so yes, the collections will transfer with the catalogue.