As several have noted, this thread could have been more specific (though I assume you wanted to leave the interpretation to the individual here). If you mean the basics everyone should have, with a little creativity that could be whittled down to 3 or 4 (.22 plinker, which can be done with a conversion on a larger auto, full size 9mm or .45, 3" or 4" medium framed revolver in .38spl or .357mag, small auto and J-frame though one could go with either or of the last two). You could mean a dream list of 10, a collectors list of 10, or what of what you have and want to have are the 10 most important. I'll answer based on the last possible interpretation.
1) My S&W 586 (6" L-frame, .357mag)
2) My S&W 65LS (3" K-frame, .357mag), should I move to a CCW state this will be the perfect carry piece.
3) a good 1911 (I have a Charles Daly which I love, I also want a Springfield Armory- if I could only have one I'd probably go with the SA, but I would want to try it first for a while before deciding which to keep)
4) My CZ 75B (though with a limit, and if I had the cash I'd be happy to replace it with a CZ 75SA or CZ 85Combat).
5) J-frame or equivelent in .38spl
*6 and 7) A brace of .45lc SA revolvers (money no object- Colt SAA, money an object- either Cimmaron SAA clones or Ruger Vaqueros).
8) A small pocket sized auto (my Bersa .380 works fine for this, a 9mm Kahr may be nice or a smaller gun in .32acp would be nice as well). I'd probably want to go with the Kahr P9 or MP9 though to free up one spot for something else as this could also double as a belt gun in a decent caliber.
*9) A blackpowder revolver (I like my cheap brass framed 1858 Rem replica but I'd prefer one with a steel frame).
10) A nice medium frame .38 (I like my Colt Police Positive Special and I'd also like another Taurus 82, but with this limit I'd only be able to have one- probably a S&W M10, M14 or M15).
* I may be willing to forgo one of the SA revolvers or the blackpowder revolver (which one would depend upon my mood, and if I will get into Cowboy Action shooting) in order to add a compact, CCW IWB or Belt pistol if I moved to a CCW state (likely a SIG 239, CZ PCR/P01, Kahr K/P 9, or Taurus PT911).
Thank G-d this is only hypothetical. Hopefully, someday when I get married this won't end up being a real life choice. If I get everything I want I'll probably own 40-50 handguns or more before I'm done. If I want to limit it more (to save money) I can probably do it in 15-20 (and sell some if I decide I want something else more). But any less than 12-15 and I would have to make some compromises I really don't want to make.