I've heard that airplanes must make steep landings at some airports in
order to minimize noise pollution or because the airport may be in a
mountainous area.  I don't like to fly and would like to avoid this
type of landing.  Can you tell me which major U.S. airports
require planes to make such steep landings?

I cannot compile such a list (I wouldn't try for $2, sorry), but San
Diego (CA) airport is certainly one of them. I remeber seeing the
airport and the city, thinking that it must be horrible for people
like you and I, who hate flying, to fly in.

Would advise you to try not to worry about that kind of thing as ANY
aircraft is likely to make a steep landing at ANY airport because of
any no. of factors of time as well as space.  For instance, a rookie
pilot may make a "less than perfect" approach to the airport which
could lead them to make a steep landing (very common).  Also, factors
such as weather and air traffic may force an aircraft to go for a
steep landing.

Steep landings are not emergency landings are considered normal
procedure, so try not to worry about it as it is unlikely you can
purposefully avoid it.

Here's a list of airports with noise abatement restrictions.

http://www.boeing.com/commercial/noise/updates.html

Landings on the parallel runways at SFO have been known to rattle people.

http://news.ottawaflyingclub.ca/_photos/SFO%20parallel.jpg
http://www.groovelicious.org/gallery/KSFO/20040104_ph_kce_sfo
http://www.groovelicious.org/gallery/KSFO/20040104_747_777_ual_sfo
http://sun.menloschool.org/~sportman/ethics/project/topics/england/SFO.jpg
http://newswire.spaceimaging.com/pagelinks/sanfran_compare_diffscale.htm

Bhavinfun --

Instrument approaches into airports, used extensively by commercial
airline traffic, are acutally standard in their descent angle.  They
are set up for gradual, controlled descents that are much less "steep"
than a visual approach can be.

Your actual hazards are much more varied.  They include descents over
terrain (politicalguru's San Diego example is a great one) or over
obstructions (Hong Kong's old approach actually had a visual target on
the top of an apartment building).  Or they include airports into
which one might be descending into snow/ice (Aspen).  Or departure
procedures with unusual turns (Aspen).  Or arrivals with sharp turns
(Juneau).

But the major air carriers actually require hours of special training
in simulators for many of these "unusual" situations before they'll
allow pilots to fly them.

Best regards,

Omnivorous-GA
PP-SEL-IR