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.