One option using the soul package (a variation of my answer to Highlighting arbitrary chunks of text connected to quotes in margins - Can this be done in TeX/LaTeX?):
\documentclass{article}
\usepackage{xcolor}
\usepackage{soul}
\definecolor{HLcolor}{RGB}{124,18,18}
\sethlcolor{HLcolor!20}
\makeatletter
\newdimen\SOUL@dimen %new
\def\SOUL@ulunderline#1{{%
\setbox\z@\hbox{#1}%
\SOUL@dimen=\wd\z@ %new
\dimen@i=\SOUL@uloverlap
\advance\SOUL@dimen2\dimen@i %\dimen@ exchanged too
\rlap{%
\null
\kern-\dimen@i
\SOUL@ulcolor{\SOUL@ulleaders\hskip\SOUL@dimen}% new
}%
\unhcopy\z@
}}
\makeatother
\newcommand\MyDBox[2][HLcolor!20]{\sethlcolor{#1}\hl{#2}}
\begin{document}
Phasellus eu tellus sit amet tortor gravida placerat. Integer sapien est, iaculis in, pretium quis, viverra ac, nunc. \MyDBox{Praesent eget sem vel leo ultrices bibendum. Aenean faucibus. Morbi dolor nulla, malesuada eu, pulvinar at, mollis ac, nulla. Curabitur auctor semper nulla.} Donec varius orci eget risus \MyDBox[cyan!30]{Duis nibh mi, congue eu, accumsan eleifend, sagittis quis, diam. Duis eget orci sit amet orci dignissim rutrum.}
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit,
vestibulum ut, placerat ac, adipiscing vitae, felis. Curabitur dictum \MyDBox[orange!30]{gravida mauris. Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna. Donec vehicula augue eu neque. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas.} Mauris ut leo. Cras viverra metus rhoncus sem. Nulla et lectus vestibulum urna fringilla ultrices.
\end{document}

A framed variation allowing to control the color for background and the frame:
\documentclass{article}
\usepackage{xparse}
\usepackage{soul}
\usepackage{tikz}
\usetikzlibrary{calc}
% The following code contains a variation of the great code by Antal S-Z
% in his answer to https://tex.stackexchange.com/a/6029/3954
%in TeX.SX
\newlength\LineWidth
\setlength\LineWidth{1.1pt}
\definecolor{HLcolor}{RGB}{124,18,18}
\sethlcolor{HLcolor}
\makeatletter
\newcommand{\defhighlighter}[3][]{%
\tikzset{every highlighter/.style={draw=#2, fill opacity=#3, #1}}%
}
\defhighlighter[fill=olive!15]{HLcolor}{.5}
\newcommand{\highlight@DoHighlight}{
\fill [outer sep = -15pt, inner sep = 0pt, every highlighter, this highlighter,draw=none]
($(begin highlight)+(0,8pt)$) rectangle ($(end highlight)+(0,-2pt)$) ;
\draw[HLcolor,line width=\LineWidth] ($(begin highlight)+(0,-2pt)$) -- ($(end highlight)+(0,-2pt)$) ;
\draw[HLcolor,line width=\LineWidth] ($(begin highlight)+(0,8pt)$) -- ($(end highlight)+(0,8pt)$) ;
}
\newcommand{\highlight@BeginHighlight}{
\coordinate (begin highlight) at (0,0) ;
}
\newcommand{\highlight@EndHighlight}{
\coordinate (end highlight) at (0,0) ;
}
\newdimen\highlight@previous
\newdimen\highlight@current
\DeclareRobustCommand*\highlight[1][]{%
\tikzset{this highlighter/.style={#1}}%
\SOUL@setup
%
\def\SOUL@preamble{%
\begin{tikzpicture}[overlay, remember picture]
\highlight@BeginHighlight
\draw[HLcolor,line width=\LineWidth] ($(begin highlight)+(0,-2pt)+(0,-0.5\pgflinewidth)$) -- ($(begin highlight)+(0,8pt)+(0,0.5\pgflinewidth)$) ;
\highlight@EndHighlight
\end{tikzpicture}%
}%
%
\def\SOUL@postamble{%
\begin{tikzpicture}[overlay, remember picture]
\highlight@EndHighlight
\highlight@DoHighlight
\draw[HLcolor,line width=\LineWidth] ($(end highlight)+(0,-2pt)+(0,-0.5\pgflinewidth)$) -- ($(end highlight)+(0,8pt)+(0,0.5\pgflinewidth)$) ;
\end{tikzpicture}%
}%
%
\def\SOUL@everyhyphen{%
\discretionary{%
\SOUL@setkern\SOUL@hyphkern
\SOUL@sethyphenchar
\tikz[overlay, remember picture] \highlight@EndHighlight ;%
}{%
}{%
\SOUL@setkern\SOUL@charkern
}%
}%
%
\def\SOUL@everyexhyphen##1{%
\SOUL@setkern\SOUL@hyphkern
\hbox{##1}%
\discretionary{%
\tikz[overlay, remember picture] \highlight@EndHighlight ;%
}{%
}{%
\SOUL@setkern\SOUL@charkern
}%
}%
%
\def\SOUL@everysyllable{%
\begin{tikzpicture}[overlay, remember picture]
\path let \p0 = (begin highlight), \p1 = (0,0) in \pgfextra
\global\highlight@previous=\y0
\global\highlight@current =\y1
\endpgfextra (0,0) ;
\ifdim\highlight@current < \highlight@previous
\highlight@DoHighlight
\highlight@BeginHighlight
\fi
\end{tikzpicture}%
\the\SOUL@syllable
\tikz[overlay, remember picture] \highlight@EndHighlight ;%
}%
\SOUL@
}
\makeatother
\DeclareDocumentCommand\MyDBox{O{HLcolor!15}O{HLcolor}m}{%
\colorlet{HLcolor}{#2}
\highlight[#1]{#3}%
}
\begin{document}
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis. Curabitur dictum gravida mauris. \MyDBox{Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna. Donec vehicula augue eu neque. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas.} Mauris ut leo. Cras viverra metus rhoncus sem. \MyDBox[yellow!15]{Nulla et lectus vestibulum urna fringilla ultrices.} Phasellus eu tellus sit amet tortor gravida placerat. Integer sapien est, iaculis in, pretium quis, viverra ac, nunc. \MyDBox[cyan!20][cyan]{Praesent eget sem vel leo ultrices bibendum. Aenean faucibus. Morbi dolor nulla, malesuada eu, pulvinar at, mollis ac, nulla. Curabitur auctor semper nulla. Donec varius orci eget risus. Duis nibh mi, congue eu, accumsan eleifend, sagittis quis, diam.} Duis eget orci sit amet orci dignissim rutrum.
\end{document}

tcolorbox, but you should look at the answers of http://tex.stackexchange.com/questions/125162/rounded-box-around-placeholder-text-that-supports-line-breaking which may contain what you want. – Thomas F. Sturm May 28 '14 at 15:05