Q:

Aside from the Jews, did Hitler have a final solution plan for other ethnicities/races in the Third Reich?

We know that Nazi ideology explicitly singled out Jews as the main reason for all Germany's problems, and planned to exterminate all of them. Nazis also persecuted gypsies, Polish people, and POWs. Did the Nazis plan to exterminate other races/ethnicities? Were there any indications of this in their writings, propaganda, letters, secret documents? For example, anything against black people? Arabs? Asians? etc?   

A:

For the Eastern Europe the Nazis had the Genaralplan Ost - the General Plan "East". According to this plan the large areas of Eastern Europe should be gradually Germanized, with the native inhabitants reduced in number, resettled and/or assimilated.
According to the plan,
Ethnic group    Percentage subject to removal
Poles           80-85%
Russians        50-60% to be physically eliminated and another 15% to be sent to Western Siberia.
Belorusians     75%
Ukrainians      65%
Lithuanians     85%
Latvians        50%
Estonians       50%
Czechs          50%
Latgalians      100%

You can notice that the Latgalians, a Baltic ethnic group in Latvia were especially disliked by the Nazis due to their historically pro-Russian attitude. The Nazis even undertook special efforts to prove their racial impurity and inferiority
As to the further plans, you should note that Hitler's attitude towards the Blacks, Asians and other peoples was much better than that towards the Slavs, the Jews and other Eastern Europeans.
In general it seems the Reich would consider it their natural right to genocide any nationalities when the area is needed for Germans.
Judging from the pattern which the Nazis established in their dealings with different ethnic groups, it is reasonable to assume that the Nazis would attempt 

To divide large peoples into smaller ethnic groups and by other criteria (religion, language dialect, region etc)
To put a "fuehrer" or "elder" in head of each ethnic group, personally responsible for carrying out the Nazi orders.
To allow a considerable autonomy of each ethnic group in their internal affairs as long as German orders are carried out.
To give expressly different rights in small and in large things to different groups, even closely related so to create envy, hubris and competition for Germans' favor.
To restrict movement of each group to their native homeland. Thus the steppe nomadic peoples would be put in steppe reservations, the mountaineers restricted to their home mountains etc. Only Germans would be allowed the right for free movement.

A:

"Intentionalism"—the view that Hitler was responsible for German racial policy (as supposed by this question's very title, "did Hitler had a final solution plan")—is not favoured amongst scholars.  Therefore, the idea of a coherent plan of racial extermination needs to be done away with.  German racial extermination policy evolved situationally and in response to local conditions.  German bureaucratic schisms encouraged such creativity.  However, repeated refrains of racialist and exterminationist policy appear again and again.  This answer considers the Slavic example.
German and NSDAP racial policy was generally quite local in nature, though following similar themes.  The Commissar order of 1941 was used as part of a generalised extermination programme relating to Slavic civillians, enacted as part of the pogrom and action programmes of 1941.
Additionally, some of the occupying authorities considered the winter 1941 food problems of Slavic civillians as not needing to be addressed due to the plan to generally starve Slavs to death West of the stop lines.  The actual food extraction policies of this period did produce significant starvation as a side effect, however, the idea of extracting the planned levels of food was ludicrous and unachievable.  (These plans were based on the idea that German standards of living ought rightly to be maintained at or near pre-war levels through mass starvation of other "racial" groups.)
Much of this culminated in the POW situation in 1941, where encamped soldiers—predominantly Slavic—were systematically neglected in a manner not undertaken in the West by the German Army.
We can be reasonably confident that with more puissance, German racial policies would have resulted in a fuller attempted genocide of people identified by Germans as Slavic.

A:

Hitler's Plans for North America
"Hitler actually held the American society in contempt, stating that the United States (which he consistently referred to as the "American Union") was "half Judaized, and the other half Negrified"[78] and that "in so far as there are any decent people in America, they are all of German origin"
"England and America will one day have a war with one another which will be waged with the greatest hatred imaginable. One of the two countries will have to disappear."[86] and "I shall no longer be there to see it, but I rejoice on behalf of the German people at the idea that one day we will see England and Germany marching together against America"."
For an extensive discussion of this entire subject - Hitler's plans for the entire world - replete with references and direct quotations, see: New Order - Nazism
I read about this many years ago - your question jolted my memory a bit so I poked around and found these references.

