keyboard shortcut in Windows 7 to center window

This is not exactly for centering, but lets you move the window left and right (and up and down) easily.

1. Focus a window.
2. Press Alt+Space.
3. Press M (for “Move”).
4. Use the arrow keys to move the window exactly where you want it.
5. Press Enter when done.

The Windows+arrow keys are quite useful here.

• (Windows)+← (Left) and +→ (Right) cycle through going to the left or right 50% of the screen, and restoring the window to its original size and position.
• +↑ (Up) maximizes the window.
• +↓ (Down) restores the window if it is maximized, and minimizes it otherwise.

I would suggest using AutoHotkey.
An example script that does exactly what you asked was already provided in an answer to another question.
Here's the code of the script:

#!Up::CenterActiveWindow() ; if win+alt+↑ is pressed

CenterActiveWindow()
{
    ; Get the window handle from de active window.
    winHandle := WinExist("A")

    VarSetCapacity(monitorInfo, 40)
    NumPut(40, monitorInfo)

    ; Get the current monitor from the active window handle.
    monitorHandle := DllCall("MonitorFromWindow", "uint", winHandle, "uint", 0x2)
    DllCall("GetMonitorInfo", "uint", monitorHandle, "uint", &monitorInfo) 

    ; Get WorkArea bounding coordinates of the current monitor.
    A_Left   := NumGet(monitorInfo, 20, "Int")
    A_Top    := NumGet(monitorInfo, 24, "Int")
    A_Right  := NumGet(monitorInfo, 28, "Int")
    A_Bottom := NumGet(monitorInfo, 32, "Int")

    ; Calculate window coordinates.
    winW := (A_Right - A_Left) * 0.5 ; Change the factor here to your desired width.
    winH := A_Bottom
    winX := A_Left + (winW / 2)
    winY := A_Top

    WinMove, A,, winX, winY, winW, winH
}

I made a slight adjustment so the bottom of the window doesn't go beneath the taskbar, and changed the windowWidth from 0.7 to 0.5.

Edit: now working with multiple monitors, and uses the work area for top and bottom values.

On a side note, WinSplit Revolution has been discontinued and replaced by a paid app called MaxTo.
In addition to being very powerful and covering much more use cases, AutoHotkey is also free and open source.