In the United States, about (one significant figure will do fine) how
many students enter college each year?  That is, what is the size of
the US's TOTAL freshman class (the sum of all freshmen classes from
every college in the country).

This table from the NCES (National Center for Education Statistics)
gives the number of first-time freshmen enrolling in fall 2004 as
2,630,000. This includes both 2-year and 4-year colleges. 2004 is the
most recent year for which these statistics are available from the
NCES.

NCES: Digest of Education Statistics Tables and Figures
http://nces.ed.gov/programs/digest/d05/tables/dt05_179.asp

My Google search strategy:

Google Web Search: "million first time freshmen" 
://www.google.com/search?hl=en&q=%22million+first+time+freshmen%22

Google Web Search: nces education statistics
://www.google.com/search?hl=en&q=nces+education+statistics

I hope this is precisely what you need. If not, please request
clarification; I'll be glad to offer further assistance before you
rate my answer.

Best regards,
pinkfreud

Thank you- that answer is just what I was looking for.

Would be interesting to see the number of yearly graduates in contrast.

Info on the number of graduates may be found here:

http://nces.ed.gov/programs/digest/d05/tables/dt05_253.asp