Do any major denominations refuse to recognize Holy Baptism in other denominations Most denominations recognize baptisms in other denominations.  (See, for example Eph 4:4-6), "one Lord, one faith, one baptism".)

The World Council of Churches Faith and Order Commission published Baptism, Eucharist, and Ministry in 1982.

Are there major Christian denominations (in the 21st century) who don't go along with this, and who require members to be rebaptized?
There are a number of different cases with regard to accepting baptisms carried out in other denominations.


Catholics Contrary to some perceptions, Catholics actually accept most baptisms carried out by other denominations. "if the proper matter and form be used and the one conferring the sacrament really "intends to perform what the Church performs" the baptism is undoubtedly valid." (Catholic Encyclopedia) The matter and form require that the person be baptized using water, and that the words "I baptize thee in the name of the Father and of the Son and of the Holy Ghost" (or equivalent) be used. This actually includes almost all Protestant sects. The major exclusions would be sects that do not believe in the Trinity, and those that explicitly baptize in "Jesus name only".
Major mainstream Protestant denominations follow similar rules to Catholics, and thus accept both Catholic and most other Protestant baptisms.
Protestant denominations that exclusively practice adult baptism almost always consider infant baptisms to be invalid, and require rebaptism of people baptized as infants. This isn't technically a rejection of the baptisms of other denominations (adult baptism of any denomination is usually accepted) but for practical purposes most baptisms by an paedobaptist denomination would be rejected.
Certain denominations have tight restrictions on method of baptism, for example insisting on immersion. A subset of those denominations will consider invalid any baptism carried out by another method, even if done as an adult. The Fellowship Baptists are an example.
Restorationist churches, such as Latter-Day Saints or Jehovah's Witnesses, consider all other baptisms to be invalid and will baptize any new convert regardless of previous baptism.