Do any major denominations refuse to recognize Holy Baptism in other denominations

In general Baptists, who believe in "Believer's Baptism" which comes only after conversion and is done only by immersion, do not even consider the sprinkling of babies to even be baptism. Thus, they do not "re-baptize" converts who may have been sprinkled, they baptize them for the first time.

• Baptists do not accept infant baptisms
• Most Nicene Christians reject non-Trinitarian baptisms.
• Oneness Pentecostals/Apostolic Christians reject Trinitarian baptisms insisting that a baptism be done in "Jesus name," that is, literally only saying the name of Jesus at baptism and not following a Trinitarian formula.

Being a former Seventh Day Adventist, I can assure you that the SDA church won't recognize baptism from other denominations especially because of some fundamental differences on the doctrines, for example the Sabbath, unclean foods, the Spirit of Prophecy (Ellen White) and the doctrine of the investigative judgment. Most of the traditional SDA Churches still apply the famous baptismal vow which can be found at Adventist Baptismal Vow. Usually, one has to be officially baptized in the SDA church in order to be a member. Blessings!

Baptism has different meanings to differnt denominations.

Some believe that in infant baptism, a parent is giving their child to Christ, and committing to raise that child as a Christian. Confirmation is when the Child chooses to continue their relationship with Christ on their own, and the parents are no longer responsible for their childs faith journey (although this does not mean that they quit! It just means that their child as "moved out of home" per-se).

Others believe that baptism is more along the lines of Confirmation in the above example - that Baptism is the individual committing themselves to Christ.

If you change denominations within the same belief structure in regards to baptism, then most churches will accept your previous baptism.

The right to Holy Communion is a very different story though, most churches will not permit you to take Holy Communion unless you go through their confirmation procedures, to prove that you know what you're doing, and that you understand what they believe about Communion, and that you agree with what they believe. For example, my wife is Catholic and I am Lutheran. She has had discussions with our church pastor, and he has admitted her to the sacrament without requiring her to become Lutheran, but it is unlikely that I would be permitted to take communion in a Catholic church.

If you are ever in doubt about whether a church will recognise your baptism/confirmation/beliefs, then the best thing to do is to ask the priest/pastor/layperson in charge. There may even be differences within denominations, depending on the personal beliefs of the pastor.

This would seem to be somewhat common among any church that believes in Believer's baptism. Since baptism under that view is a profession of faith in Christ, it would seem that any previous baptism based upon the same faith would be valid. However, if there is a large doctrinal difference between the former and current fellowship (and thus the believer accepts a new "Gospel") there would be reason to baptize that person as a new believer. It also would be appropriate to re-baptize those who may have experienced an infant baptism as there would have been no profession of faith at that time.

Mormon's don't recognize any baptism of other faiths because they believe the person doing the baptizing needs to have the correct authority.

Specifically, the priesthood of God. Hebrews 5:4 states, "And no man taketh this honour unto himself, but he that is called of God, as was Aaron." Aaron was called by revelation, and ordained by Moses laying hands on his head. This is how the Priesthood is bestowed in the LDS Church. (See Heb 1-4)

There are a number of different cases with regard to accepting baptisms carried out in other denominations.

1. 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".
2. Major mainstream Protestant denominations follow similar rules to Catholics, and thus accept both Catholic and most other Protestant baptisms.
3. 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.
4. 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.
5. 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.