End each line with a %. This will gobble the line-feed and all whitespace at the beginning of next line. Thus you'd get
\documentclass[option1,%
option2,%
option3,%
option4,%
option5,%
option6,%
option7]{article}
to do what you want it to.
Edited To Add: As Geoffrey points out in a comment to this answer, in this context, this solution is overkill. Using % at the end of a line will always gobble up the newline and the leading whitespace — however, this is (as Geoffrey points out) irrelevant unless in a context where initial whitespace is influential. Thus, in a \documentclass, it can be omitted and Kit's original code used; while in a case like
\begin{tikzpicture}
\foreach \p/\x/\y in {%
0/1/2,%
2/3/4,%
3/4/5,%
4/5/6,%
} {
\node [coordinate] (p\p) at (\x,\y) {};
}
% Do stuff with the defined coordinates
\end{tikzpicture}
it becomes relevant, as otherwise the whitespace would be included with the definition of \p, and destroy the crafted coordinate names.
Plenty similar examples outside of TikZ exist — this was the example I could think of the quickest where it becomes relevant.