According to Wikipedia:
The charismatic movement is the international trend of historically mainstream Christian congregations adopting beliefs and practices similar to Pentecostalism. Fundamental to the movement is the use of spiritual gifts (charismata).
Among Anglicans, the charismatic movement emerged in 1958; it reached Lutherans and Presbyterians in 1962. Among Roman Catholics, it spread around 1967. Methodists became involved in the charismatic movement in the 1970s.
In my own words, the charismatic movement emphasizes "spiritual gifts" (such as healing, prophecy, speaking in tongues, etc. -- see 1 Corinthians 12 for a more exhaustive list) and "ecstatic/mystical experiences" (such as the baptism with the Holy Spirit). In more extreme congregations, people may even display very extreme and odd behaviors, such as shaking or trembling violently, behaving like animals, etc.
Is there anything like this in Islam?