How many professional sports leagues are there in the United States? 
And can you provide me a link to a ranking of U.S. professional sports
leagues by total revenue or profit?  For example, I assume that the
NFL is No. 1 and that MLB, the NBA, and the NHL are No. 2, No. 3, and
No. 4, but what sports league is No. 5, No. 6, etc.?

Generally speaking, there are four "major" sports leagues which are
the ones you named (NBA, MLB, NFL, NHL).  Some would argue for the
inclusion of MLS, however they do not compete on the level of the four
majors.

Others to consider include  the WNBA; NASCAR, CART and IRL (if
including motorsports); the AFL (Arena Football League); MISL (Major
Indoor Soccer League).  WUSA (Women's United Soccer Association)
folded last year, however they are consider re-launching at some point
in the future.

An excellent resource for this type of data is Street & Smith's Sports
Business Journal (www.sportsbusinessjournal.com which offers a free
trial).  They release studies annually including the "League Report
Card" (generally October each year) and "By the Numbers" (a book of
sports data available for $75).

In terms of ranking by popularity (not what you asked for, I realize),
the order of the big 4 in 2002 was NFL, MLB, NBA and (distantly) NHL.

I have the 2004 By the Numbers in front of me, but alas not the 2003
League Score Card.  I will try to find it to answer you question about
revenue.