As Anastasios said, ROCOR has of late been carrying on intense dialogue with the Moscow Patriarchate in hopes of officially establishing communion between the two Churches.
As for what ROCOR has done:
-Produced saints recognized by the entire Orthodox world.
-Translated and/or printed numerous Orthodox texts in the English language.
-Spoke out about the persecution of Christians in the Soviet Union when most other Churches were quite silent about it.
-Sent tens of thousands of religious books to Russia during the Soviet period. (I was told that in one year Holy Trinity Monastery spent something like $50,000 on postage from doing this!)
-Maintainted traditional monasticism and parish life. Along with this, ROCOR's members have contributed greatly to the growth of monasticism in America.
-Spoken out against excessive and false ecumenism.
-Brought a great many people to the Orthodox faith, including one convert(Fr. Seraphim Rose) who is seen by many as a saint.
-Glorified St. John of Kronstadt, St. Xenia of Petersburg, St. John of San Francisco, the Royal Martyrs of Russia and the New Martyrs of Russia.
-And, most importantly, and summing up the above happenings- they've brought Orthodox Christians to salvation. That's the goal of the Church. Perhaps ROCOR hasn't been as "flashy" or "worldly wise" as some in the Church today, but I do believe they've kept a faithfulness to the traditions of the Church, and helped to maintain Orthodox piety and the normal ascetic Christian life when other Orthodox bodies in the West were straying from this path.
As for ROCOR and the Western Rite. Presently, I believe there is only one Western Rite institution of ROCOR- a monastery in Rhode Island.