Diagnostics about LaTeX installation

tlmgr info

lists all TeXLive packages with a preceeding i, if already installed. Or use

tlmgr list --only-installed

You can also create a complete list as pdf (run with lualatex --shell-escape <file>):

\documentclass[fontsize=11pt,paper=a4,pagesize]{scrartcl}
\usepackage{luacode,ltablex}
\begin{document}
\section*{Installed packages in \TeX{}Live}
\begin{luacode}
local fh,err = io.popen("tlmgr list --only-installed")
if not fh then
  texio.write(err)
  os.exit(-1)
end
tex.print("\\begingroup\\footnotesize\\noindent")
tex.print("\\begin{tabularx}{\\linewidth}{@{} r @{.~} l X @{}}")
local i=0
for line in fh:lines() do
  i = i + 1
  tex.print(i .. "&" .. line:gsub("^i ", ""):gsub(": ", "&", 1)
    :gsub("\\", "\\textbackslash{}"):gsub("_", "\\_"):gsub("$","\\\\"))
end
tex.print("\\end{tabularx}\\endgroup")
fh:close()
\end{luacode}
\end{document}

I have no idea how it can be done for MiKteX.

A pdflatex version; run with -shell-escape.

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{xparse}

\ExplSyntaxOn

\NewDocumentCommand{\listpackages}{}
 {
  \krlmlr_list_packages:
 }

\ior_new:N \g_krlmlr_read_stream

\cs_new_protected:Nn \krlmlr_list_packages:
 {
  \ior_open:Nn \g_krlmlr_read_stream { |"tlmgr~list~--only-installed" }
  \ior_map_inline:Nn \g_krlmlr_read_stream
   {
    \__krlmlr_process_line:n { ##1 }
   }
 }

\cs_new_protected:Nn \__krlmlr_process_line:n
 {
  \__krlmlr_process_line_aux:w #1 \q_stop
 }
\cs_new_protected:Npn \__krlmlr_process_line_aux:w #1~#2~#3 \q_stop
 {
  \noindent\texttt{\tl_to_str:n { #2 }}~\tl_to_str:n {#3}\par
 }
\ExplSyntaxOff

\begin{document}

\listpackages

\end{document}

(Just the first few entries and not the whole 76 pages.)