In the movie Patch Adams, describe how Patch shows three different types of love for people: companionship, romantic love, & friendship.

After having met the "real" Patch Adams a few years ago
and hear about his amazing organization that attempts to bring joy and laughter to
places fraught with tragedy, I feel honored to answer this question.  Patch Adams does,
in fact, exhibit all three types of love you mention in your question.  Let's deal with
them separately.

First, companionship.  Donning nothing but
a clown's nose, Patch is able to brighten the days and lives of sick children by
visiting the children's ward of the hospital quite often.  His silly, slapstick humor
takes their mind off of their troubles as they await and recover from serious surgeries
and (sometimes terminal) diseases.  There are smiles all around when Patch enters the
room, where only gloom and loneliness is apparent
beforehand.

Second, romantic love.  Although not part of
the "real life" story of Patch Adams, the movie character of Patch has a very strong
love for Carin Fisher (a definite cold fish at first).  Patch woos Carin in the same way
he gives the children in the ward companionship:  through humor.  Carin Fisher opens up
through her ability to laugh at Patch, and she is finally feeling her own romance toward
Patch blossom when her life is ended far too soon (by a highly disturbed patient she is
attempting to help).

Finally, friendship.  Some of the most
moving scenes in the film in my opinion are between Patch Adams and the character of
Bill Davis, a terminally ill cancer patient.  For what seems to be a VERY long time,
Bill is irate and even violent towards Patch's attempts at humor and cheer.  However,
little by little, Bill begins to adore Patch, confiding in him as a friend.  Bill shares
revelations about his family, his illness, and even his spirituality to Patch, ... and
there is no more tearful scene than when Patch Adams sings his own version of "Blue Sky"
as Bill passes on.

I'll admit, absolutely every time I hear
the line, "Blue skies smiling at me, nothing but blue skies do I see," I always think of
Patch Adams singing to Bill as one of the different types of love you mention in your
question.  Therefore, in conclusion, I need to mention a different "type" of love that
is very important to both the real Patch Adams and the character in the movie:  love of
the poor.  Both through his institute to help those without insurance and through his
mission to bring humor to places of tragedy, Patch Adams makes his great love for
humanity apparent.