I like Strauss too but I suspect Stravinsky is considered to be "higher-rated" but this is just a guess on my part.
I also like Mussorgsky but again IMHO I suppose he aint in the same league as your "3M" conglomerate.
My "Big R" would have to be Rossini.
Have you seen this movie? It's really good!
Thanks for the info NimzoRoy.
No I haven't had a chance to see that film yet. Of course each person has their favourites and as you say a lot of people might prefer Stravinsky over J.Strauss Jr. but in a list of the " Big-S " names we must include Schubert as well. Under the " Big-R " names I do like Rossini, for one thing he wrote a lot of beautiful Music for the Violin. Rimsky-Korsakov should also be in the " Big-R " group as well. Returning to the Bach Family one should remember that several of Johann Sebastian's sons also became Composers so they might be thought of as a " multiple " name entry I guess. 
Well, Strauss was prolific, but the most kick-ass Waltz surely belongs to Offenbach (of Can-Can fame)
To the Bs, add in Bartok. For S, dump J. Strauss in favor of Richard Strauss (no relation), and add Shostakovich.
A great W is Wagner, of course, father-in -law of a great L, Liszt.
Thanks for the recent posts.
Yes Bartok should be on our list and of course Richard Wagner and Shostakovich as well. Smetana needs to get into the list on the basis of his " Moldau " alone I think.
Getting back to Waltzes we do need to include Offenbach as well. Thomas Koschat cannot be ignored either because his " Snow Waltz " ( Schneewalzer ) is a very beautiful item also.
rooperi was Offenbach stoned when that picture was taken - or was it taken in the carnival fun house with all the distorted mirrors?
Incidentally, if you're looking for a "K" composer, I am one.
Here is one of my works: http://allhands.com/mp3/cornell%202012-rose.mp3
Thanks for the posts.
JamieKowalski: Well we do have some room for Composers in the " Ks " so I'm sure thatwe can fit you in. There were a couple of well known Conductors in the " Ks " but I don't think that they wrote all that much Music.
I thought of Khatchaturian, Kabelevski, and Korngold, but I wasn't sure others would know them so well.
Thanks for the info JamieKowalski. Korngold is a bit familiar to me, not the others so much. On the Conductors side I was thinking of von Karajan and Otto Klemperer ( yup, father of Werner ).
In the title of this thread we have the name of Bach. I gather that Bach ( the Elder ) was best known in his day as a Organist as well as a Composer and I very much enjoy the Music that he wrote for the Pipe Organ. The Pipe Organ is sometimes referred to as the King of Musical Instruments, nothing else has that sort of range and volume.
Some more names of note to include are Ravel and Handel. Rimsi-Korsakoff had been listed earlier and might be considered under the letter R, however he could also have his own heading under R-K lol.
Off course another great R is Rachmaninov.
http://www.metrolyrics.com/decomposing-composers-lyrics-monty-python.html
The "official" Big-S (at least in German music theory) are Schütz, Schein and Scheidt - for those of us who like the really old stuff. 
Schütz is really one of the all-time greats and one of my personal favorites.
Thanks for the recent info, some very good names there.
I've realized that I forgot to mention an item the other week. I did mention that several members of the Bach Family were involved in Music. However in the case of Johann Strauss Jr. one should also mention Johann Strauss Sr. even tho in this case it is the son that is the better known person.
In a few threads around here I have mentioned that my short term memory has never been all too good. I'm often losing track of my keys or my glasses and the problem relates to names as well. While looking back over this thread I noticed that I had a little memory-lapse back in the 3rd post. I meant to refer to Verdi in regards to the beautiful Violin Music whereas Rossini is of course best known for composing the beautiful " William Tell Overture " ( yup I certainly put my foot in it that time lol ).
I have a thread on the go here featuring Classic Rock & Roll in which other types of Music do get mentioned from time to time and so I thought why not go with a thread for Classical Music as well. So I listed the " Big 3-B Names ", then we also have the " Big 3-M Names " with Mozart, Mendelssohn & Mahler. Of course we must add the " Big-T " as in Tchaikovsky, the " Big-H " as in Hayden and many many others. My favourite " Big-S " name would have to be Johann Strauss Junior as his Waltzes are such happy tunes. When I hear such Music as The Emperor Waltz, The Blue Danube or Wine Women & Song I cannot help but get into a good mood.