How might we update or enhance our product visual identifier/logo to best reflect our brand?
The Apache OpenOffice brand reflects the following attributes:
The following visual elements are associate with the Apache OpenOffice products:
No wrong answers here, just a collection of sketches realizing the visual elements.
Graham Lauder - Graphical Text for Logo text
This is another example of a text graphic created in inkscape used instead of some type of typeface. It's a San Serif type font and can be modified as an svg. 
PNG version: 
This logo proposal changes makes use of a new font and logo scheme to present the word OpenOffice by updating the orb as a flat surface and placing a "donut" hole (which represents the open nature of AOO as an open source project) in the orb along with our trademark gulls effectively making it an "O" which anchors the words "Open" and "Office" but with the use of a single "O". The logo also makes use of a new typeface.
Michael Acevedo - Concept Logo for AOO 4 Proposal #2 (12-19-2012)
The second logo proposal for Apache OpenOffice 4 is more conservative, conventional, and simplistic than the previous logo proposal; which makes the new open office logo more recognizable among the community. The new logo proposal makes use of an updated OpenOffice orb which now rests on four squares that represents the four main applications associated with an office suite (Blue= Writer, Green= Calc, Orange= Impress, and Violet= Base). In addition the orb now is surrounded by a white belvel emboss ring that makes the logo look more like a pin and actually makes it stand out of the four background squares
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Michael Acevedo - Concept Logo for AOO 4 Proposal #3, 4, 5, 6, and 7 (12-20-2012)
Below there are 5 additional logos for the Apache OpenOffice project, all of these follow a similar language to logo proposal 2. 
A design quite different from the Gulls and even the parameters used. The logo applies more basic elements with a second version that is more complex. It tries to emulate some symbolism of continuity and dynamic evolution. Is not meant to be a finished design but the inspiration to think different about logos and image of the product.
A more complex version with something that is between feathers or the flow of water. It add some dynamism and speed to the continuity symbol.
Some suggestions on improving the fonts and color combination has already been contributed. A more rounded and contrasting font might improve the impact of the logo.
Sample document attachment: sample_document.odt