It’s difficult to customize this right from your theme, and I suspect that’s why I was unable to locate any flexible solutions through the Wordpress forums or Google. The easiest way is to edit the original function itself. Be warned: new Wordpress installations will overwrite this fix.

Locate general-template.php

Open the wp-includes folder from the root of your Wordpress install. Open the file general-template.php with a text editor and locate the wp_get_archives function. Find the following line:
 

820
821

$text = sprintf(__('%1$s %2$d'), $wp_locale->get_month($arcresult->month), $arcresult->year);
//

In Wordpress 2.8.4 this is on line 820. The default date format is the full textual representation of the month and the full year. Example: January 2009.

Alternative Date Formats

Short textual representation of month

Example: Jan 2009

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821

$text = sprintf(__('%1$s %2$d'), $wp_locale->get_month_abbrev($wp_locale->get_month($arcresult->month)), $arcresult->year);
//

Numeric representation of month with leading zero

Example: 01 2009

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821

$text = sprintf(__('%1$s %2$d'), zeroise($arcresult->month, 2), $arcresult->year);
//

Numeric representation of month, no leading zero

Example: 1 2009

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821

$text = sprintf(__('%1$d %2$d'), $arcresult->month, $arcresult->year);
//

Two digit representation of year

Example: January 09

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821

$text = sprintf(__('%1$s %2$s'), $wp_locale->get_month($arcresult->month), substr($arcresult->year, 2));
//

Adding Flourishes and Changing Order

Additional formatting can be applied by just changing ‘%1$s %2$d’ in that line, where %1$s represents the month and %2$d represents the year.

Punctuation between month and year

These examples use a slash. Replace with dot or dash as desired.

Example: 01/2009

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821

$text = sprintf(__('%1$s/%2$d'), zeroise($arcresult->month, 2), $arcresult->year);
//

Example: 01/09

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$text = sprintf(__('%1$s/%2$d'), zeroise($arcresult->month, 2), substr($arcresult->year, 2));
//

Abbreviated Year

Example: January ‘09

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821

$text = sprintf(__('%1$s /'%2$s'), $wp_locale->get_month($arcresult->month), substr($arcresult->year, 2));
//

Reversed Month and Year

Example: 2009 January

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821

$text = sprintf(__('%2$d %1$s'), $wp_locale->get_month($arcresult->month), $arcresult->year);
//

Mix, Match, Enjoy!

There are more combinations than I can reasonably post here, but I hope this helps you figure out how to get the exact date format you want.