Free windows tiling manager (similar to ShiftIt or divvy) that can be installed without admin privileges
I use scripts like these:

try
    tell application "Finder"
        set b to bounds of window of desktop
    end tell
    set item 1 of b to ((item 3 of b) / 2)
    set item 2 of b to 22
    tell application (path to frontmost application as text)
        set bounds of window 1 to b
    end tell
end try




try
    tell application "Finder" to set b to bounds of window of desktop
    set item 2 of b to 22
    tell application (path to frontmost application as text)
        set bounds of window 1 to b
    end tell
on error
    try
        tell application "System Events" to tell (process 1 where it is frontmost)
            click (button 1 of window 1 where subrole is "AXZoomButton")
        end tell
    end try
end try


They don't require access for assistive devices to be enabled (other than for the on error block in the second script). They don't work with all windows though, and I don't know what will happen if you have multiple displays.

Automator services are supported out of the box and you can create them on a non-admin account, but as of 10.8 there is a bug where the keyboard shortcuts for Automator services don't always work until you hover over the services menu from the menu bar. There is also a relatively long delay before Automator services are run.



See this answer for other ways to assign shortcuts to scripts. I use FastScripts, which is free for up to 10 keyboard shortcuts and doesn't require administrator privileges.