Protestants do perform many of the rites that the Catholic church considers Sacraments, but only two, Baptism and Communion, are considered Sacraments by the majority of Protestants. These two are the only two rites that are conducted using the formula given to us by Jesus.
Luther, as is usual, took the first step:
We have now finished the three chief parts of the common Christian doctrine. Besides these we have yet to speak of our two Sacraments instituted by Christ, of which also every Christian ought to have at least an ordinary, brief instruction, because without them there can be no Christian; although, alas! hitherto no instruction concerning them has been given.—The Large Catechism IV, 1
Luther suggests here that without Baptism and the Sacrament of the Altar (i.e. Holy Eucharist), there can be no Christian. This criteria leaves out Marriage, since many Christians have not and will not be married.
(I don't know were that particular criteria comes from however. The Bible doesn't explicitly establish rules for what is considered a "Sacrament".)
He also rejects sacramental penance (i.e. Reconciliation) at the start of his 95 Theses:
Our Lord and Master Jesus Christ, when He said Poenitentiam agite, willed that the whole life of believers should be repentance.
This word cannot be understood to mean sacramental penance, i.e., confession and satisfaction, which is administered by the priests.
Yet it means not inward repentance only; nay, there is no inward repentance which does not outwardly work divers mortifications of the flesh.
The argument here (which is fleshed out in later points) seems to be that confession is not limited to a rite performed by a priest and is therefore not a sacrament. (There is some confusion here since Luther seems to label repentance as "the third Sacrament" in The Larger Catechism IV, 74, but in 75 he clarifies that "it is really nothing else than Baptism.")
Joseph Stump's An Explanation of Luther's Small Catechism states there are three criteria for a rite to be labeled a Christian Sacrament:
The Command of Christ;
The Use of Earthly Elements;
The Communication of a Heavenly Gift.
Note that these are not explicitly stated by Luther himself, however. If I recall correctly, this was the criteria I was taught in my Evangelical Covenant confirmation.
For many Protestants, however, the fundamental issue with Sacraments in general is that we reject a specialized priesthood. In the Old Testament, priests were set aside from the Levites, who were themselves set aside from within Israel, which was itself a people set apart by God. According to the New Testament, these distinctions have been removed:
As you come to him, a living stone rejected by men but in the sight of God chosen and precious, you yourselves like living stones are being built up as a spiritual house, to be a holy priesthood, to offer spiritual sacrifices acceptable to God through Jesus Christ.—1st Peter 2:4-5 (ESV)
Exactly what this passage means practically is a matter of dispute, but many Protestants view the "priesthood of all believers" to mean that all believers have direct access to God via Christ, our High Priest. (I know that the Catholic Church does affirm the "priesthood of all believers", but I don't understand the position myself. Please correct and forgive me if I mischaracterize here.) We submit to the authority of Christ Jesus and to each other, but not a church hierarchy. While we often do have some form of church structure, it is usually seen as a practical, social construct and not as a result of Apostolic Succession. Therefore, the distinction between Sacraments and ordinary Christian rites are less clear. Some traditions eliminate the distinction altogether.
Finally there is an important distinction between Baptism and Communion compared to the other possible Sacraments: Jesus himself gave us the formula (or words) we use to practice them. For Baptism:
And Jesus came and said to them, “All authority in heaven and on earth has been given to me. Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, teaching them to observe all that I have commanded you. And behold, I am with you always, to the end of the age.”—Matthew 28:18-20 (ESV)
And for Communion:
For I received from the Lord what I also delivered to you, that the Lord Jesus on the night when he was betrayed took bread, and when he had given thanks, he broke it, and said, “This is my body which is for you. Do this in remembrance of me.” In the same way also he took the cup, after supper, saying, “This cup is the new covenant in my blood. Do this, as often as you drink it, in remembrance of me.” For as often as you eat this bread and drink the cup, you proclaim the Lord's death until he comes.—1st Corinthians 11:23-26 (ESV)
As far as I can tell, the other potential Sacraments were not commanded by Christ in the same way. Therefore, while we do practice marriage, ordination, visitation of the sick and dying, repentance, and confirmation (along with many other rituals), we don't view these as equal in significance to the rites instituted by Christ Jesus.