Was the N.E.P. of Russia successful in terms of economics?

Actually, Wikipedia contains a reasonably good answer to this (clearly ill-posed) question.

The background:

Urban workers formed the core of Bolshevik support, so the exodus posed a serious problem. Factory production severely slowed or halted. Factories lacked 30,000 workers in 1919. To survive, city dwellers sold personal valuables, made artisan craft-goods for sale or barter, and planted gardens. The acute need for food drove them to obtain 50–60% of food through illegal trading. The shortage of cash caused the black market to use a barter system, which was inefficient. Drought and frost led to the Russian famine of 1921, in which millions starved to death, especially in the Volga region, and urban support for the Bolshevik party eroded.[10] When no bread arrived in Moscow in 1921, workers became hungry and disillusioned. They organized demonstrations against the Bolshevik Party's policy of privileged rations, in which the Red Army, Party members, and students received rations first. The Kronstadt rebellion of soldiers and sailors broke out in March 1921, fueled by anarchism and populism. In 1921 Lenin replaced the food requisitioning policy with a tax, signaling the inauguration of the New Economic Policy.

In other words, NEP was introduced in order to prevent the country (and the rule of the Communist Party) from collapsing. As such, it was an obvious success. Furthermore:

Results.

After the New Economic Policy was instituted, agricultural production increased greatly. In order to stimulate economic growth, farmers were given the opportunity to sell portions of their crops to the government in exchange for monetary compensation. Farmers now had the option to sell some of their produce, giving them a personal economic incentive to produce more grain. This incentive, coupled with the breakup of the quasi-feudal landed estates, surpassed pre-Revolution agricultural production. The agricultural sector became increasingly reliant on small family farms, while heavy industries, banks, and financial institutions remained owned and run by the state. This created an imbalance in the economy where the agricultural sector was growing much faster than heavy industry. To maintain their income, factories raised prices. Due to the rising cost of manufactured goods, peasants had to produce much more wheat to buy these consumer goods, which increased supply and thus lowered the price of these agricultural products. This fall in prices of agricultural goods and sharp rise in prices of industrial products was known as the Scissors Crisis (due to the crossing of graphs of the prices of the two types of product). Peasants began withholding their surpluses in wait for higher prices, or sold them to "NEPmen" (traders and middle-men) who re-sold them at high prices. Many Communist Party members considered this an exploitation of urban consumers. To lower the price of consumer goods, the state took measures to decrease inflation and enact reforms on the internal practices of the factories. The government also fixed prices, in an attempt to halt the scissor effect.

The NEP succeeded in creating an economic recovery after the devastation of World War I, the Russian Revolution, and the Russian Civil War. By 1925, in the wake of Lenin's NEP, a "... major transformation was occurring politically, economically, culturally and spiritually." Small-scale and light industries were largely in the hands of private entrepreneurs or cooperatives. By 1928, agricultural and industrial production had been restored to the 1913 (pre-World War I) level.

So, surely the results were a mixed bag of successes and failures.

Lastly:

Influence

Pantsov and Levine see many of the post-Maoist economic reforms of Chinese Communist Party leader Deng Xiaoping towards a socialist market economy during the 1980s as influenced by the NEP: "It will be recalled that Deng Xiaoping himself had studied Marxism from the works of the Bolshevik leaders who had propounded NEP. He drew on ideas from NEP when he spoke of his own reforms. In 1985, he openly acknowledged that 'perhaps' the most correct model of socialism was the New Economic Policy of the USSR."

So, if, one uses as a criterion of success the proverb "Imitation is the Sincerest Form of Flattery," then yes, NEP was quite successful, just not in Soviet Russia.

On the other hand (since all experts should be 2-handed economists), of course, NEP was a failure, see Samuel Russel's answer.

No. It is generally considered to be a failure.

The chief problem was the recurrent scissor's crises due to the agricultural sector not being incorporated into a commodity economy. As the price of agricultural goods declined, peasants would withdraw from the market economy and the (very few) Kulaks did likewise, reverting from small rural capitalists to rich peasants. When the market economy did not operate purely in the interests of the peasantry, they retreated from the market, creating imbalances in the agricultural to industrial price balance.

See the Nove Millar debate: Millar, James R. and Alec Nove. “A Debate on Collectivization: Was Stalin Really Necessary?” Problems of Communism 25 (July/August 1976): 49-62.

Normatively, if we consider the purpose of the Bolshevik party to usher in a classless society through the agency of the working class—and if we consider this to be an "economic" goal—it was a god awful disaster and the worst case of ratting out the class to the boss by non-workers in a so-called worker's party ever seen. Simon Pirani's work demonstrates that Lenin dismantled the workers state in 1921, replacing it with a Party state. Any of the sociology of the NEP will show that institutions such as one man management dismantled significantly much of the property control that workers had over plants. So the NEP smashed the institutions of the workers' state by dismantling the political power work place committees held, and it significantly dismantled the economic ownership of the workplaces by works committees.

Finally, by the late 1920s "ultralefts" in the lower orders of the Bolshevik party were demanding collectivisation, and many urban workplaces were demanding a campaign of terror against the countryside due to the long term lack of adequate food supply to the cities. If the NEP was meant to be a long term and positive economic process, these political problems couldn't have arisen from below. (See Conquest or Solzhenitsyn)

A recommended reading here is Farm to Factory: A Reinterpretation of the Soviet Industrial Revolution by British economic historian Robert Allen. I don't know the literature in detail, but Allen is generally very well respected for his work. (Google finds a review of the book here). From Amazon's page on the book:

Although the Russian economy began to develop in the late nineteenth century based on wheat exports, modern economic growth proved elusive. But growth was rapid from 1928 to the 1970s--due to successful Five Year Plans. Notwithstanding the horrors of Stalinism, the building of heavy industry accelerated growth during the 1930s and raised living standards, especially for the many peasants who moved to cities. A sudden drop in fertility due to the education of women and their employment outside the home also facilitated growth.

While highlighting the previously underemphasized achievements of Soviet planning, Farm to Factory also shows, through methodical analysis set in fluid prose, that Stalin's worst excesses--such as the bloody collectivization of agriculture--did little to spur growth. Economic development stagnated after 1970, as vital resources were diverted to the military and as a Soviet leadership lacking in original thought pursued wasteful investments.

For more details: read the book! :-) (if you are on a university network you might find a paper on the same subject by the same author here)