Correctly scaling a tikzpicture

You could try using the command \resizebox. You enclose the tikzpicture environment in one of those and then in is scaled. Like this:

\resizebox{<horizontal size>}{<vertical size>}{%
    \begin{tikzpicture}

    \end{tikzpicture}
}

If you want the image to be scaled proportionally, you can give one of the sizes and put ! in the other. There is also a \scalebox{<factor>}{...} macro which allows scaling by a factor. This works well except when the tikzpicture has a matrix command, and the columns are separated by &, in that case, you can change the column separator using the option ampersand replacement in the matrix options as stated in the pgfmanual.

Alternatively use the adjustbox package which provides an adjustbox environment which also allows resizing and scaling while allowing for special content including catcode changes required for verbatim text and the aforementioned &.

Pgf has two different types of transformations: coordinate transformations and canvas transformations. When using \begin{tikzpicture}[scale=0.50], you are applying coordinate transformation. All coordinates will be scaled, whereas individual objects (text, line thickness, rounding of corners etc) will not scale. Most of the time that is what you want, you do not want to scale carefully typeset pieces of text, you do not want to make lines ridiculously thick, or too thin to actually print.

If you want to scale everything, you have to use a canvas transformation. For that, pgf has a command \pgftransformscale{}. You can also use the pgflowlevelscope environment:

\begin{tikzpicture}
  \draw (0,0) rectangle (6,6); %create a bounding box to reserve space
  \begin{pgflowlevelscope}{\pgftransformscale{5}}
     \draw (0,0) -- (1,1) node[right]{$x$};
  \end{pgflowlevelscope}
\end{tikzpicture}

You can also use \pgflowlevelsynccm which synchronizes the canvas transformation matrix with the current coordinate transformation matrix, for example like this:

\begin{tikzpicture}[scale=5]
  \draw (0,0) rectangle (1.2,1.2); %create a bounding box to reserve space
  \pgflowlevelsynccm
  \draw (0,0) -- (1,1) node[right]{$x$};
\end{tikzpicture}

Note that because pgf does not (cannot) keep track of the canvas transformations (they are performed by the backend), you will have to make sure there is enough space in your picture for the scaled objects. In the examples above, I try to reserve space by drawing a bounding box first, before applying the canvas transformation. There are other problems with canvas transformations, and I do not recommend using them without carefully reading appropriate parts of the pgf manual.

I include this answer more as an explanation of what is going on, another, preferable answer using \resizebox has already appeared.

You can use the option "transform shape" for the whole picture, a scope or a single node. Example:

\begin{tikzpicture}[scale=2, transform shape]
  \draw rectangle (1,1) node {foo};
\end{tikzpicture}

\begin{tikzpicture}[scale=2]
  \draw rectangle (1,1) node {bar};
\end{tikzpicture}

But be careful, this will not solve all your cases with scaling tikz pictures, e.g."rounded corners" will not scale. The tikz authors (general) advice is not to scale graphics.