UNIX and Linux, just mount the remote filesystem using NFS or Samba. The Oracle server will treat the remote filesystem like it's own as long as the permissions are OK. You shoul be able to use UTL_FILE ok.
Windows 2000, map a network drive to the app server and use UTL_FILE to write to it.
Windows NT 4.0, No way There is an unfixed bug in this version of windows which prevents Oracel writing to a mapped drive.
You will have a problem with UTL_FILE in the default NT setup because the WinNT user SYSTEM can not access network drives. A solution is to run the Instance (and possibly Listener) NT services as a non-SYSTEM WinNT user, member of the local administrators group and with "log on as a service" priviledge. It works for both mapped drives and "url" format. (I tested with 22.214.171.124 under NT 4.0 SP6a). You should think about impact of password changes though!