How can I turn an R data frame into a simple, unstyled html table?

The xtable package can generate HTML output as well as LaTeX output.

# install.packages("xtable")
library("xtable")
sample_table <- mtcars[1:3,1:3]
print(xtable(sample_table), type="html", file="example.html")

gives, in the file example.html:

<!-- html table generated in R 3.0.1 by xtable 1.7-1 package -->
<!-- Fri Jul 19 09:08:15 2013 -->
<TABLE border=1>
<TR> <TH>  </TH> <TH> mpg </TH> <TH> cyl </TH> <TH> disp </TH>  </TR>
  <TR> <TD align="right"> Mazda RX4 </TD> <TD align="right"> 21.00 </TD> <TD align="right"> 6.00 </TD> <TD align="right"> 160.00 </TD> </TR>
  <TR> <TD align="right"> Mazda RX4 Wag </TD> <TD align="right"> 21.00 </TD> <TD align="right"> 6.00 </TD> <TD align="right"> 160.00 </TD> </TR>
  <TR> <TD align="right"> Datsun 710 </TD> <TD align="right"> 22.80 </TD> <TD align="right"> 4.00 </TD> <TD align="right"> 108.00 </TD> </TR>
   </TABLE>

This could be further simplified with more options to xtable and print.xtable:

print(xtable(sample_table, align="llll"), 
      type="html", html.table.attributes="")

gives

<!-- html table generated in R 3.0.1 by xtable 1.7-1 package -->
<!-- Fri Jul 19 09:13:33 2013 -->
<TABLE >
<TR> <TH>  </TH> <TH> mpg </TH> <TH> cyl </TH> <TH> disp </TH>  </TR>
  <TR> <TD> Mazda RX4 </TD> <TD> 21.00 </TD> <TD> 6.00 </TD> <TD> 160.00 </TD> </TR>
  <TR> <TD> Mazda RX4 Wag </TD> <TD> 21.00 </TD> <TD> 6.00 </TD> <TD> 160.00 </TD> </TR>
  <TR> <TD> Datsun 710 </TD> <TD> 22.80 </TD> <TD> 4.00 </TD> <TD> 108.00 </TD> </TR>
   </TABLE>

(which could be directed to a file with the file argument to print.xtable as in the previous example.)

to_html_table<-function(dataframe){
 tags$table(
  tags$thead(tags$tr(lapply(colnames(dataframe), function(x) tags$th(x)))),
  tags$tbody(
   apply(dataframe,1, function(x) { tags$tr(lapply(x, function(y) tags$td(y)))})
  ))
}

A prettier but slower option:

library(htmlTable)
htmlTable(iris)