In most bibliographic styles, the suffixes Jr. and Sr. go after both names of an author in the bibliography, preceded by a comma:
Gauch, Hugh G., Jr. (2012). Scientific method in brief. Cambridge: Cambridge University Press.
It seems like most BibTeX styles have struggled to get this right. I've also found now that the default behavior of biblatex doesn't follow the standard either. In the example below, the suffix Jr. is placed according to the general guidelines.
\documentclass{article}
\usepackage[style = authoryear-comp]{biblatex}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@BOOK{gauch2012,
AUTHOR = "Gauch, Jr., Hugh G.",
TITLE = "Scientific method in brief",
YEAR = "2012",
LOCATION = "Cambridge",
PUBLISHER = "Cambridge University Press"}
\end{filecontents}
\addbibresource{\jobname.bib}
\begin{document}
\nocite{*}
\printbibliography
\end{document}

I've tried other permutations of the order First name, Last name, Jr. in the .bib file, but I haven't found one that gives the desired output.
According to the comments to Have the BibTeX styles gotten the placement of a name's "junior" part wrong?, both biblatex-apa and biblatex-chicago have the desired order, so it is at least possible to implement this in biblatex. How can I do it?
EDIT
When implementing Guido's suggestion, the default layout of subsequent authors, which is first name - last name, changes to last name - comma -- first name.
\documentclass{article}
\usepackage[style = authoryear-comp]{biblatex}
\DeclareNameFormat{author}{%
\usebibmacro{name:delim}{#5#1}%
\ifblank{#5}{#1}{#5 #1}\addcomma\addspace
#3\isdot
\ifblank{#7}{}{\addcomma\addspace #7}\isdot
}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@BOOK{gauch2012,
AUTHOR = "Gauch, Jr., Hugh G.",
TITLE = "Scientific method in brief",
YEAR = "2012",
LOCATION = "Cambridge",
PUBLISHER = "Cambridge University Press"}
@BOOK{chomsky1968,
AUTHOR = "Noam Chomsky and Morris Halle",
TITLE = "The sound pattern of English",
YEAR = "1968",
LOCATION = "New York, NY",
PUBLISHER = "Harper \& Row",
SERIES = "Studies in language"}
\end{filecontents}
\addbibresource{\jobname.bib}
\begin{document}
\nocite{*}
\printbibliography
\end{document}


Jr.at the end than there are styles that don't. By "struggle to get it right", I'm referring to the designedBibTeXstyles that fail to putJr.at the end even though the style sheets they are designed for do so. – Sverre Nov 01 '14 at 15:46