The highest salaries in the Soviet Union were paid out to the highest ranking party and military officials. In the 1980s General Secretary Gorbachev received a monthly salary of around 1,500 rubles (the equivalent of around $2,500 using official exchange rates), while other Politburo members received around 1,000-1,200. The top generals and minister of defense received around 2,000 rubles, various entertainers and cultural important persons in the Soviet Union received around 1,000 per month. By comparison, a general medical practitioner on the average received around 130 Ruble a month, which was less than that of a bus driver.
In some ways the question itself is somewhat problematic, because in the Soviet Union the monetary system isn't as meaningful as in a capitalist country. Often times it's not enough for one to have the monetary means to acquire desired goods, but you would also need blat, or connections with the right people to sell it to you. This often involved "trading" favors in which both parties would be conducting illicit transactions to procure the goods/services they desire from each other. This could be qualified as "corruption" but it was also a widely engaged practice in the Soviet Union and an inbuilt part of the system.
Wealth also existed in the form of perks. For instance, being a ranking official in the party meant you received a state owned Dacha and a large apartment which cannot be bought. You would be assigned a car and driver paid for by the state. Your children would be able to go to the best schools and you would be admitted to the best hospitals. You would be given access to special shops selling rare goods at special prices. You would have access to spas, resorts, entertainment, foreign and domestic travel off limits to the average person: often at government expense.
Also as before mentioned, being an apparatchik give you more power, connections and therefore means to trade favors with others to acquire goods and services that one desires. Therefore it is very difficult to quantify this in purely monetary terms.
Source: Daily Life in the Soviet Union by Katherine B Eaton
Equity and Efficiency in "Mature" Socialist Societies by Nicolas Spulber
After reading through most of these comments I have a few more questions about these "favors" doctors or white collared workers may recieve. A few comments mentioned how these favors could be more than just basic services, but actual "goods." So let's say a soviet doctor is doing a lot of favors and is racking up all kinds of tangible goods, maybe even a car or two. Was that allowed in the Soviet Union? Could someone own a couple cars yet still make their 130 rubles a month? Would a government official come by and question where all this property came from? I guess I am really asking what property ownership meant in the Soviet Union. This further connects with the original question, could someone like a doctor amass wealth through getting a bunch of tape players or other random goods?
What would be the wealth they possessed in terms of the free amenities that were not cash money available to them?
Probably the best example I know of would be Erno Rubik, the inventor of the Rubix Cube:
http://articles.orlandosentinel.com/1986-12-01/lifestyle/0270440083_1_rubik-cube-erno
In the above 1984 article it states that his salary was $200 per month but he was earning royalties of $30,000 per month. As others have stated, this doesn't really mean very much when the supply of goods are constrained but I can't think of a better example to answer the question about the richest (in terms of personal holdings) that anyone could become in the Soviet Union.