How can I use aliases in the Go to Folder dialog? Can I somewhere define aliases that I can use in the Go to Folder dialog?

More specifically, can I somehow setup Finder such that when I type Pictures it goes to the ~/Pictures directory?
There's no nice way to set up an alias in the Finder like you can in the Terminal, but you can set up text-expansion abbreviations in the Keyboard System Prefs' Text tab.

I prefer Typinator myself, as it is much more flexible and full-featured than the system prefs.

You could also roll-your-own utility using a script-runner utility and Applescript.