Is there a `for each` loop in primitive (La)TeX?

A more “primitive” way in LaTeX, that also avoids the issues with grouping one gets with \foreach, would be

\makeatletter
\def\basiccolors{%
  black,blue,brown,cyan,darkgray,gray,green,lightgray,lime,%
  magenta,olive,orange,pink,purple,red,teal,violet,white,yellow%
}
\def\do@def#1{%
  \expandafter\newcommand\csname command#1\endcsname{%
    \textcolor{#1}{Some text including the string #1}%
  }%
}
\@for\next:=\basiccolors\do{\expandafter\do@def\expandafter{\next}}
\makeatother

Note that no spaces are allowed in the list of items.

It's much easier with expl3:

\usepackage{expl3}

\ExplSyntaxOn
\NewDocumentCommand{\makecommandsfromlist}{mm}
 {
  \clist_map_inline:nn { #1 }
   {
    \cs_new:cpn { command ##1 } { #2 }
   }
 }
\ExplSyntaxOff

\makecommandsfromlist{
  black, blue, brown, cyan, darkgray, gray, green,
  lightgray, lime, magenta, olive, orange, pink,
  purple, red, teal, violet, white, yellow
}
{\textcolor{#1}{Some text including #1}}

You could use \@for or an expl3 list but often a more convenient (and a lot more efficient in terms of expansions) technique is to use a different structure which allows you to execute the list with no separate loop macro, this is explained in appendix D of the texbook and used in several places in latex (look for \@elt usage) I'll use \\ here.

\documentclass{article}

\def\thecolors{\\{black}\\{blue}\\{brown}\\{cyan}\\{darkgray}\\{gray}\\{green}\\{lightgray}\\{lime}\\{magenta}\\{olive}\\{orange}\\{pink}\\{purple}\\{red}\\{teal}\\{violet}\\{white}\\{yellow}}
\usepackage{xcolor}

\begin{document}


{%
\def\\#1{\expandafter\gdef\csname command#1\endcsname{%
    \textcolor{#1}{Some text including the string #1.}}}%
    \thecolors
}


\commandblue

\end{document}