Hello
Me and my brother tried to connect with each other on Baldur's Gate 1 gog version but we failed to do it. Each time there was an error with the connection problem. We've tried either with and without Hamachi but it wasn't enough, Client sometimes asked for password, sometimes announced error without it. We've got the same version of BG1, no mods etc.
Thank you for your answer

Are you both using GOG versions and are they DLed from the same account?

There are plenty of possible causes.
Try to start the game windowed (add -windowed to the shortcut parameters) as there are issues starting multiplayer games in fullscreen. You can switch to full screen once it's running (press Alt+Enter).
Add the game's folder to your firewall's exceptions, so all of the games executables are allowed to communicate with the network.

Check this thread, it is helpful for hosting:
http://www.gog.com/forum/baldurs_gate_series/windows_7_64_bit_cant_host_multiplayer

An alternative to Hamachi would be GameRanger, just in case you want to try something else.

Me and my friend played through Baldur's Gate 1 without any problems using Gameranger. Just make sure both of you has set the game to windowed mode when the host starts the game from the character arbitration screen at the beginning of each session. After that, the game can be fullscreen for the rest of the session.