I can't find a way to close a view panel, in particular the horizontal at the bottom, is pretty useless to me at this moment.
That is the Logic Editor at the bottom, (you probably opened it accidentally as it's not normally in the Default scene as you have it). In your case here, look in the corner of the panel where the little lines are.. (these are called the viewport handles and are always in the upper top-right or lower bottom-left).
Left click the handle and drag down, an arrow will overlay the view as a sort of confirmation, just drag it down and it will 'close' that view.
Likewise, the process to open one is the same. You can also create new windows with these, Just Shift click on the handles in either corner and drag it to 'tear' it out that view into its own window. (this just makes a copy of that view in its own window, the original stays the same)
NB: A good point to further note is that to expand or collapse a view into another. They must be of the same width or height. Meaning, if the top has two views and the bottom has one wide one, you wouldn't be able to expand the bottom one.
An alternative to iKlsR's answer:
You can close a panel by right clicking on the line between the two pannels (i.e. the shadowed area. Your mouse will turn into a double-sided arrow when you hover) and clicking join area: