The macro \HighlightRestOfCurrentLine below allows you to highlight to the end of the current line:

References:
Notes:
This does require two runs. First one to determine the locations, and the second to do the drawing. Although I have a feeling this should be doable in just one run.
The magic numbers for determing the edge of the page are obtained by using \layout from the layout package.
The \tikzmark is from Adding a large brace next to a body of text.
Code:
\documentclass{article}
%\usepackage{layout}
\usepackage{tikz}
\usetikzlibrary{calc}
\newcommand{\tikzmark}[1]{\tikz[overlay,remember picture] \node[baseline] (#1) {};}
\newcommand{\HighlightRestOfCurrentLine}[1][]{%
\tikzmark{Start}%
\begin{tikzpicture}[overlay,remember picture]
\coordinate (EdgeOfText) at ($(current page.west |- 0,0) + (1.0in+\hoffset+\oddsidemargin+\textwidth,0.3ex) + (0.1em,1.6ex)$) ;
\draw [draw=none,fill=green!50, #1] ($(Start)+(0,-0.6ex)$) rectangle (EdgeOfText);
\end{tikzpicture}
}%
\begin{document}%\layout
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Sed at dignissim eros.
Morbi faucibus sit amet felis a accumsan. \HighlightRestOfCurrentLine Aliquam
dapibus pellentesque dui, vitae aliquam turpis semper eget.
Donec egestas leo nibh, at malesuada leo congue non.
Cras laoreet lectus sed tortor laoreet, ac aliquet nibh condimentum.
Nam elementum ante non nunc facilisis porttitor. Nullam non suscipit lorem.
Sed arcu dui, accumsan et pretium dictum, venenatis id metus.
Mauris massa lacus, vehicula
vitae \HighlightRestOfCurrentLine[fill=none,draw=gray, ultra thick] blandit ac,
fermentum vitae ligula. Maecenas ultricies, tortor a sodales ullamcorper,
erat lorem semper leo, vel pretium felis arcu ut velit. Aenean viverra
lacus at nisi malesuada luctus. Maecenas libero odio, luctus et blandit
vitae, commodo in turpis. Duis nisi enim, gravida id libero id,
sollicitudin volutpat purus. Curabitur rhoncus risus euismod arcu venenatis,
\HighlightRestOfCurrentLine[red!25]non elementum mi lobortis.
Pellentesque quis leo eu nunc malesuada condimentum. Ut dictum iaculis
aliquam. Nunc tincidunt a ligula in adipiscing. Praesent
\HighlightRestOfCurrentLine[fill=none,draw=blue, dotted, ultra thick]ultricies sem
odio, eget pellentesque mi faucibus vitae. Class aptent taciti sociosqu
ad litora torquent per conubia nostra, per inceptos himenaeos.
Sed ullamcorper massa risus, non commodo dolor eleifend quis.
Mauris ultrices lorem a orci hendrerit tempor. Sed fringilla mattis fringilla.
\end{document}
\def\bla#1\par{\textcolor{red}{#1}}– Bordaigorl Jun 12 '14 at 15:10\paror even a blank line directly (leaving a blank line after#1and the{). But it doesn't work if you want it to work just with that line (even if there is no blank line following). `\def\delimitedbyblankline#1{Something with “#1”}`.
– Manuel Jun 12 '14 at 15:38