Linux and Windows

Firefox

You'll really like something like Mozilla Weave or Xmarks to synchronize your browser experience. This way, when you switch from one computer to another, you won't lose your history or bookmarks.

Sharing Keyboard and Mouse

Synergy

Synergy allows you to share your keyboard and mouse by combining the desktops into a continuous desktop. When you move your mouse off the edge of the screen, it will show up on your other computer.

I prefer to use Linux as the Synergy server and any other computer on my desktop, like my laptop or whatnot, as the client.

You can tunnel Synergy over SSH for an added bit of security. Usually, this is unnecessary since you'll be behind a firewall anyway, and the Linux server pretty dang secure.

Logging into Linux from Windows

Text interface: SSH

Your best bet for a text interface is SSH.

Text + Apps: SSH + X11 Forwarding

If you have an X Server on your windows box (like Xming), and you allow X11 connections over SSH, you can even open applications. For instance, you type "firefox" in the SSH console, and the Firefox app opens up on your windows desktop, as if you were running it locally.

Obviously, you need a good, fast connection with low latency to make this work well.

Login to your Linux Box Graphically from Windows

Xming allows you to run a full-screen app. With XDMCP, you can even login through X to your Linux box and get the full linux experience. Again, you'll need a good, fast connection with low latency to make this work well.

Logging into Windows from Linux

Rdesktop or KRDC. This allows you to open a window in your Linux session that is a Windows session on your Windows box.

VNC?

I don't recommend VNC anymore. It was nice in its day, but it's no longer necessary.

Sharing Files

The obvious ideas (FTP, HTTP, etc...) work OK, if you're getting the files from Windows to Linux.

You can also use windows networking and Samba on your Linux box, both as a client and as a server.

Nowadays, you should be storing your files in a more permanent place in the cloud. See drop.io and Amazon's S3 for ideas.