It did not achieve too much. The movement had three main problems: ideological, economical, and organisational. Non-Aligned Movement had no solid ideological base: all they could agree on was harsh criticism of Western capitalism and opposition to being under effective Soviet control. Economically there were very few ties between countries of the Non-Aligned Movement: most countries were poor and agricultural, there was very little intra-movement trade that would push the countries together and make the movement a coherent political unit. Organisationally, no NAM-wide institutions or organisations were established (think along the lines of UNESCO or UNICEF or UNHCR and so forth), which again meant that there was quite little cooperation between the countries of Non-Aligned Movement, especially compared to the West or the Soviet Bloc.

Why was this important? Well, as it was mainly a bunch of countries with little integration there were very few common interests between the countries. Yugoslavia was interested in maintaining its fragile situation literally between Western and Soviet blocs, African and Asian countries were most keen on securing development aid and pushing decolonisation further. Egypt was strongly against Israel, Southeast Asian countries had naturally less interest in what was happening in Israel. In the Non-Aligned Movement summit of 1979 in Havanna, the then Cuban leadership of the movement tried to push the countries to support a pro-Soviet position, while the Yugoslav leader Tito had for decades struggled against Soviet dominance. Iraq and Iran even ended up fighting a bloody war in the 1980s, and as the Non-Aligned Movement had no military force of its own it could not just stop the bloodshed.

So understandably they did not have much accomplishments, at least not much that you could actually point at. They did demand the American president Lyndon Johnson to hold unconditional talks with North Vietnam during the Vietnam War, this motion was supported by 17 countries of the Non-Aligned Movement, and this is considered by some to be one of the high moments of the whole movement [don't remember the exact source here, but IIRC it was Stevan Pavlowitch, Yugoslavia [imaginative name, eh?]]. If you count the creation of a "third way" between the West and the Soviet Bloc as an accomplishment, then the Non-Aligned Movement certainly achieved something as quite a lot of countries managed to go through the Cold War without ending up too strongly aligned to either bloc.

This answer is based on a Yugoslav point of view, so my apologies if I have accidentally misled you here. Also sorry if I rambled a bit, but I find the whole movement quite fascinating and I think that some sort of a background explanation was necessary to make it clear why it had little achievements.

Sources: a university lecture on Yugoslavia and the Non-Aligned Movement [is this allowed as a source or should I provide more information?]; John R. Lampe, Yugoslavia as History