If such exists, I would like a list of at least 6 or more movies
(old or new) that meet the following criteria.
1. subject matter that pulls on heart strings
2. tearjerker
3. heartwarming or happy ending
4. sex or necessary violence is ok, but has no superfluous violence

Hello colorado39-ga!

This was a fun (if slightly depressing at times) question to research!
I even enlisted the help of movie buff friends to run through my list
and make suggestions. Of course, this list is highly subjective, and
what may be a ?happy ending,? ?heartwarming,? or a ?tearjerker? to one
may not qualify to another. You asked for six movies, but I figure I
can give you more (18, I believe). With that said, here is my list of
movies.

- - - - - - - - - - - - - - - - - - - -

A Beautiful Mind
An Affair To Remember
Because of Winn Dixie
Charlotte?s Web
Cinderella Man
The Color Purple 
Dead Poets Society
E.T.
Field of Dreams
Gladiator (F.Y.I.--one may argue that some of the violence in this is gratuitous)
Hope Floats
Les Miserables 
The Notebook
Remember The Titans
Return of the Jedi
Return of the King
Rudy
Shawshank Redemption


The Internet Movie Database is a great site to get information on
movies, including plot summaries, cast listings, etc. If you register
with their site for free you will have access to user posts as well.
www.imdb.com

This is a link to a thread posted on lost-forum.com entitled ?favorite
tearjerker movies.? I found it quite useful in making my list.
http://lost-forum.com/archive/index.php/t-1385.html

There was another excellent forum posting asking men to discuss movies
that made them cry. It was interesting reading for sure!
http://www.belowtopsecret.com/thread210353/pg1

- - - - - - - - - - - - - - - - - - - -

I hope you find the information that you need. If you have need of
further clarification, please let me know how I can help.

Sincerely,
Boquinha-ga

Search terms:
Happy tear jerker movies
"tear jerker" movies "happy ending"

I am sorry it took so long to respond.  These are wonderful for the
need.  Thanks for both the specifics, the commentors and the links.

1. I Am Sam - this movie really touched me. It's about a mentally
handicapped man fighting for her daughter, so she is not taken away by
social services.
2. The Green Mile - about a big African American man who went to
prison because he "killed" two little girls. Set in the time when
racial discrimination was evident in America.
3. Remember the Titans - heartwarming movie based on a true story.
Denzel Washington played a football coach for a mixed-race team. Set
in 1971.
4. The Notebook - a very beautiful love story. I cried so many times.
5. Philadelphia - about a once respected attorney fired because he's got AIDS. 
6. Forrest Gump

Forrest Gump is a good suggestion. I'd add "Babe."

"Old Yeller" is a real tearjerker.

"Amy" Australian movie starring Rachel Griffiths featuring Nick
Barker(1998)   About a little girl who stops talking after witnessing
a tragedy.

Any "Lassie" movie.

"Black Beauty"

"Beaches"

"Airport 75"

"Poseidon Adventure" original starring Shelley Winters (1972)

"Amy" is my personal favourite.

A bit of a challenge if only because #1 and #2 can be pretty
subjective--note the absence of sports movies in my list--and because
some of the best examples that come to my mind of #1 and #2 don't have
#3, at least not in a conventional sense (e.g., Life is
Beautiful)--and vice versa. But a few thoughts:

Little Women (Wynona Ryder version)
Shawshank Redemption
Howl's Moving Castle
In America 
Love Actually 
Finding Neverland (okay, not a "happy" ending, but if Beaches can qualify...)
The Lord of the Rings trilogy

My wife just clopped me on the head and hissed "A.I." at me. She's
right, this is a powerful movie. When Jessica leaves David (Haley Joel
Osmet) in the woods, begging and crying as he runs after her...  
*sniff*  Or when the cops get Gigolo Joe...

Other possibilities:

Gone With The Wind (upbeat, if not heartwarming or happy ending)
Casablanca (I think it's a snooze, really)
Anything with Veronica Lake and without Sonny Tufts.

Can I swap "Beaches" for "Starman"? (starring Jeff Bridges)

Casablanca, of course, and
Gone with the Wind,

also 

Sabrina,
Roman Holiday
Love in the Afternoon

  (is my age showing?)

A Walk To Remember

"The Spirit Of St. Louis", starring Jimmy Stewart. My eyes tear up
every time he comes in for the landing at Le Bourget field in Paris.

Thank you so very much for the 5 stars and the generous tip, too! I'm
so glad that you find the list so useful! Thank you very much!

Sincerely,
Boquinha-ga

I'll add my two cents and say that "Field of Dreams" and "Return of
the King" are defininte testosterone tear jerkers.

Good work boquinha!

And another fun one. This place is great. What a shame that it's closing. :(