Single Player:
Space Rangers 2: Rise of the Dominators
X-Com: UFO Defense
Mercenaries

All these games are very large, X-Com and Space Rangers are randomized every time you play them while Mercenaries is just so large and good I'd definately have it with me.

Multiplayers:
BOTS

Not any other than that, mainly because I'm not into multiplayer myself.

Singleplayer:

Rome total war (with rome total realism installed)
Civilizations (CivNet)
Deus Ex

Multiplayer (in case there would be another castaway with computer)

WarCraft 2
Age Of Empires 2
Ghost recon

Fallout 2
thief
thief 2 and hercules

mp:
cs
cs
and cs

There is always a way to get to the internet, as long as you have the connection. Telnet.exe would be one, for example.

The whole multiplayer and internet part is flawed and a bad idea, IMHO. That's why I didn't answer that part.

I can`t believe that no one will bring an adult game on an deserted island.... LOL

Who cares about logic in this case. Just pretend this is how it is :)

We can assume that you are not the only person on the island, but you can only connect to other people on the island if they bring computer close enough to connect to your LAN.

Single player games: Minesweeper, Master of Orion, and XCOM: Enemy Unknown (in that order).

Multiplayer: This is a really tough call, as all my favorite multiplayer games are boardgames. I would have to say a java editor to write client-implementations of my favorite boardgames.

I am hungry is there food here or am I doomed to play video games untill I die of starvation.

Single player:
Max Payne 1
Shadowgate(the games similar to this like Daja Vu ect.)
Maniac Mansion(Several different ending that is replay value babby

I do not play multi-players as sadly I have dial up.

SP:
1. Chessmaster 10th Edition (so I can finally learn to play chess decently)
2. Oblivion (and the TES-Toolkit off course, so I can make more Oblivion for myself)
3. Gothic (simply love it)

MP:
1. Anarchy Online
2. World or Warcraft (never played it, but this seems about the right time to get started) :D
3. Call of Duty 2

Obviously, it's best not to simply choose your favourite games, but rather great games with high replay value. I cheated a little by picking 2 SP and 4 MP, but if need be I'd just play CM in single-player.

Single-Player
1) X-com - Terror From The Deep
2) Civilization

Multi-Player
1) Vampire, The Eternal Struggle (actually a computerized version of the card game)
2) Vampire, The Masquerade - Redemption (for the great storytelling possibilities)
3) Star Trek - Birth Of The Federation (or the fan-made sequel, if it's finished by then)
4) Championship Manager (not sure which version)