The Protestants were the first to introduce the catechism as we know it today. One example of this is Martin Luther's
"Small Catechism" and "Large Catechism" -- the "Small Catechism" was aimed at laymen and the "Large Catechism" at Lutheran clergy.
The Catholic Church countered by producing what is known as the
"Roman Catechism", or Catechism of the Council of Trent, as the first universal Catholic catechism. It is still a very important and foundational work. It covers less ground than the new CCC but is unassailable and definitive.
There have also been catechisms prepared by local diocese. The most popular of which is the
"Baltimore Catechism". It is aimed at schoolchildren and is divided up into four editions covering the same ground but in increasing depth.
Thus the "Baltimore Catechism 1" says:
Q. Why did God make you?
A. God made me to know Him, to love Him, and to serve Him in this world, and to be happy with Him for ever in heaven.
It is the same in Baltimore Catechism 2 but 3 adds a greater explanation in the following question:
Q. Why is it necessary to know God?
A. It is necessary to know God because without knowing Him we cannot love Him; and without loving Him we cannot be saved. We should know Him because He is infinitely true; love Him because He is infinitely beautiful; and serve Him because He is infinitely good.
The "Baltimore Catechism 4" or "Teacher's Guide" contains a very long explanation:
Q. Why did God make you?
A. God made me to know Him, to love Him, and to serve Him in this world, and to be happy with Him forever in the next.
"To know" Him, because we must know of a thing before we can love it. A poor savage in Africa never longs to be at a game or contest going on in America, because he does not know it and therefore cannot love it. We see a person and know him; if he pleases us we love him, and if we love him we will try to serve him; we will not be satisfied with doing merely what he asks of us, but will do whatever we think might give him pleasure. So it is in regard to God. We must first know Him—learn who He is from our catechisms and books of instruction, but especially from the teaching of God's ministers, the Holy Father, bishops and priests. When we know Him, we shall love Him. If we knew Him perfectly, we should love Him perfectly; so the better we know Him the more we shall love Him. And as it is our chief duty to love Him and serve Him upon earth, it becomes our strict duty to learn here whatever we can of His nature, attributes, and holy laws. The saints and angels in Heaven know God so well that they must love Him, and cannot therefore offend Him.
[...Three more paragraphs follow...]
The Catechism of the Catholic Church is the new universal catechism. It was published in 1992 and is very strongly influenced by the documents of Vatican II. There is some controversy surrounding it because of this. It was edited by Cardinal Joseph Ratzinger (now Pope Benedict XVI) and Abp. Christoph Schönborn of Vienna, Austria. The latter has made a number of controversial statements in support of homosexuality, divorce, contraception and an abandonment of clerical celibacy.
So the "Small Catechism" is a Lutheran catechism and therefore is not appropriate for Catholics, unless of course you are referring to St. Robert Bellarmine's Catechism or another small catechism (e.g. Penny Catechism or Catechism of St. Pius X). The Roman Catechism and the Baltimore Catechism are both very solid and well-accepted -- the Roman Catechism was originally aimed at clergy, particularly pastors, and was written in the 16th century. The Baltimore Catechism is aimed at schoolchildren (though books 3 and 4 are fine for adults as well) and was written in the late 19th and early 20th century (revised several times). The Catechism of the Catholic Church (CCC) is the most recent catechism and covers a lot of ground, however, there is some controversy around it.