I just changed my old google searchbox with Adsense's official search box.
Well... Almost for the official part, since as most people know, Google's HTML has never been valid. So I found myself forced to change some bits of it so it would validate as correct XHTML1.1 :)
This is what I found in Adsense's Terms & Conditions. Apparently I can't do that :( ....
Implementation and Operation of Ads, Search Results, and Referrals. You agree to comply with the specifications provided by Google from time to time to enable proper delivery, display, tracking, and reporting of Ads, Links, Search Results, Referral Buttons, and Google Brand Features (as defined in Section 12 below) in connection with Your Site(s), including without limitation by not modifying the JavaScript or other programming provided to You by Google in any way, unless expressly authorized in writing by Google (including by electronic mail).
(...)
(ii) edit, modify, filter or change the order of the information contained in any Ad, Link, Ad Unit, Search Result, or Referral Button, or remove, obscure or minimize any Ad, Link, Ad Unit, Search Result, or Referral Button in any way;
(....)
You will not modify, adapt, translate, prepare derivative works from, decompile, reverse engineer, disassemble or otherwise attempt to derive source code from any Google services, software, or documentation, or create or attempt to create a substitute or similar service or product through use of or access to the Program or proprietary information related thereto.
Oh well...