People have discussed this before here on Enotes. The following thread offers actual names and achievements.
The one thing from Islam, which I think we can say for sure influenced the West, is the poetry of Omar Khayyam. Here in California, it is required reading just like Shakespeare or Homer.
During the period of 600-1450, West got influenced by the Islamic civilization. The Islamic civilization introduced a different way of living which was definitely superior than the one which existed before the islamic civilisation. But on the contrary, it created a bitter feeling in the minds of the Christians towards Muslims.
The superior Muslim culture which the West came to know about during the crusades, made the Western people embrace Islam with open arms and it gave birth to the people's self-consciousness in the West. Intellectually the West, achieved a lot of success during the 12th and 13th centuries, by imitating the science and learning of the Islam civilisation.
To take forward several scientific investigations in various fields, the Arabs used the method of observation and experimentation. This inductive technique of inquiry later on, was adopted by the West.
The Islamic civilisation also influenced the Western philosophy and gave a humanistic bend to the minds of the people in the West. Earlier philosophy and science was thought to be totally opposed to religion in the West. But Muslim thinkers, helped the West to develop in a better manner by harmonizing religion or faith with reason.