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According to the page on Mini Nukes, 95 in total.

They can also occasionally be found in vendors inventory for purchase. Personally I have never used one, but after doing the entire main quest, including Broken Steel, as well as Mothership Zeta, I have collected 90 total. I have yet to do Point Lookout, The Pitt or operation anchorage, so I’m guessing that number of 95 may not be entirely accurate as I’m sure I haven’t found every last one available up till now.ReapTheChaos 22:32, January 29, 2010 (UTC)