How do you get mathbb{1} to work (characteristic function of a set)?

Another option is to use bbold package.

documentclass{article}
usepackage{bbold}
begin{document}
[ mathbb{1} ]
end{document}

Though it ruins the letters.

documentclass{article}        
usepackage{anyfontsize}         
% For documents in 10pt, 11pt or 12pt     
% defone{mbox{1hspace{-3.85pt}fontsize{11}{14.4}selectfonttextrm{1}}} % 10pt    
defone{mbox{1hspace{-4.25pt}fontsize{12}{14.4}selectfonttextrm{1}}} % 11pt    
% defone{mbox{1hspace{-4.75pt}fontsize{13}{14.4}selectfonttextrm{1}}} % 12pt    
begin{document}    
You can use either $one$ or $one{A}$ or $one_{A}$.
end{document}

I'm surprised no one has mentioned this, but you can use the unicode-math package. Note that you need Xe(La)TeX or LuaLaTeX to use this package.

documentclass{article}

usepackage{amsmath}
usepackage{unicode-math}

begin{document}
    $mathbb{1}$
end{document}

This worked for me:

usepackage{mathbbol}

+mathbb{1}+

Actually, I'm using LyX, so I put usepackage in the preamble and then simply used mathbb with a 1 inside a formula box. It still displays as `rubbish' but renders fine as PDF.

If you don't like the discordance in LyX, you can say something like

defbbone{mathbb{1}}

in the preamble, and then use bbone in your document, or variants on this theme.

My 2c.

A new solution: use newtxmath package.

With code:

usepackage{newtxmath}

$vmathbb{ABCDEFGHIGKLMNOPQRSTUVWSYZ}$
$vmathbb{abcdefghijklmnopqrstuvwxyz}$
$vmathbb{0123456789}$

which results:

Also, this solution is compatible with the ACM Template's whitelist restriction, since there're no need to import other packages, the document class asmart already imported the newtxmath. However, there's some bugs if you do not explicitly import the newtxmath, if you try to type blackboard bold 1 in this situation, try vmathbb{s}, this outputs the right format.

Here's the document of the newtxmath: http://ctan.mirror.colo-serv.net/fonts/newtx/doc/newtxdoc.pdf

Update: In new version of TeX (2020), I found that vmathbb{1} worked correctly.

Playing some necromancy here, the answer looks very different in 2021. I especially advise against using bbm, as the accepted answer suggests, since the old-fashioned font format it loads will come out pixelated in a PDF, and nobody prints DVIs out on paper any more.

I’d recommend using unicode-math in LuaTeX when you can, and legacy fonts when you have to. Nearly all OpenType math fonts support mathbb{1} and Bbbone out of the box. Few if any come with a bold version that supports boldsymbol{mathbb{1}}, but you can fake it if you need it:

documentclass{article}
tracinglostchars=2
usepackage{unicode-math}

setmathfont{NewCMMath-Book}
setmathfont{NewCMMath-Book}[
  version=bold,
  FakeBold = 1.2 ]

begin{document}
[ mathbb{1} boldsymbol{mathbb{1}}
]
end{document}

If your publisher still requires you to use PDFTeX, or you should wish to, the mathalpha package provides a consistent interface for loading and scaling math alphabets, including blackboard bold and bold blackboard bold. Here are the options that ship with TeX Live and at least partially work:

(Note that you do not need to define Bbbbone this way in your own document! I put this in the template to simplify testing.)

documentclass{article}
usepackage{amsmath}
usepackage[bb=dsserif]{mathalpha}
usepackage{bm}

pagestyle{empty}
    
newcommandBbbbone{%
  ifdefinedmathbbb%
    mathbbb{1}%
  else%
    boldsymbol{mathbb{1}}%
  fi}

begin{document}
[ mathbb{1} Bbbbone
]
end{document}

The dsserif alphabet is the only free one I know of that supports both blackboard-bold and bold-blackboard-bold digits in Type-1 format, and that a package can load without changing your other fonts. You will probably want to scale this to match your math font, with the bbscaled= package option.

With bb=pazo instead of bb=dsserif:

With bb=fourier:

With bb=esstix:

With bb=boondox:

There are other legacy packages not available through mathalpha (as of February 2021). Here are some of the more important ones that have not already been mentioned.

The cmathbb package is an attractive outline font based on Computer Modern bold.

With usepackage[varbb]{newtxmath}, you get the same alphabet as in Xovee’s answer, but replacing the standard mathbb:

There is a similar option for newpxmath (although this is incompatible with bm).

documentclass{article}
usepackage{amsmath}
usepackage[varbb]{newpxmath}

pagestyle{empty}

newcommandBbbbone{%
  ifdefinedmathbbb%
    mathbbb{1}%
  else%
    boldsymbol{mathbb{1}}%
  fi}

begin{document}
[ mathbb{1} Bbbbone
]
end{document}

There is yet another blackboard bold alphabet available through newtxmath and newpxmath, with the vvarbb package option:

The stix and stix2 packages load an alphabet similar to boondox. (Which is a fork of the STIX fonts.) Here is what you get with usepackage{stix2} instead of mathalpha: