I have a local server setup with debian installed.

My wife and I travel some and I have never trusted free internet service at condos and Hotels. So I was wondering if one could setup a local server with VPN. VPN into this server from where ever you are and use the programs installed on this server? Can two people login to this server at the same time? My home service is 30mbs so speed should not be an issue.

Is this doable?

http://wiki.debian.org/OpenVPN/

And do a search for "debian vpn" in your favourite search engine which will yield many results too.

Many people do that for similar reasons.

Some other ways may be to use remote desktop type apps over some secure connection/tunnel.

You are actually limited by the 'thinnest' part of the cxn between wherever you are in the world and your home ie if you are in some 3rd world country using dial-up, then that's your limit even if your house has FTTH...

This may or may not solve your problem.
I have stayed in 'tels on business trips that offered free WIFI, but (and they did NOT tell you this up front) block or restrict VPN and RDP traffic so that you CANNOT secure your connection. Generally the bandwidth was not anything to write home about either.

You really have to wonder about a company that would like very much for you to NOT secure your information! What business are they REALLY in?

I no longer let my company travel agent pick my lodging.

Ask your questions BEFORE you travel, and change your lodging or make other plans to secure your life, belongings, and data well before departure.

[ -- sigh -- Even that is not foolproof. I once booked the family into a well-known 4star for vacation months ahead. Arrived to find the management changed (the previous week)and there were goats running through the lobby. Don't even ask what the room smelled like. We were lucky enough to be able to shift to another place very quickly. ]