Yes, you can move databases between machines.
Make sure OS and Oracle-Version are the same!
If all paths are identical you can simply copy the files, set ORACLE_SID and startup the database.
if you change paths you have to do a ALTER DATABASE RENAME FILE '/full/path/and/filename' TO '/new/full/path/and/filename'; in MOUNT status for all datafiles and redo-logfiles.
Just take care of some spread files like oratab, start/stop-scripts etc.