Strongly recommend LapLink - have been using it for years, and if it won't work, then the computers simply aren't connected. Apart from straightforward "copy to" or "move to" functions, it also has a very good bidirectional synchronisation function. It comes with a set of very pretty cables (yellow for parallel and blue for serial connections).
It can also be used in a "local" mode which offers considerably more functionality than Windows Explorer (the synchronisation mode is simply not available in Windows Explorer).
The only problem I've had is when certain other programmes (Palm HotSync for example) grab the port you're trying to use and won't let go. Solution is simple - turn HotSync off. I am still using Laplink 95 (version 7.5) - I guess there must be a later version by now. V7.5 offers remote connection by modem but have never had occasion to use it - don't really want to leave my telephone connected to a modem - one of these days I should invest in one of these fancy line switches which can differentiate between incoming voice, FAX and data signals.
I do have a shelfware copy of PC Anywhere - found it a bit idiosynchratic - wouldn't always do what I wanted it to do.
LapLink is one of those applications that I use from time to time and it always just works - I really cannot recommend it too highly.