Swedish Christianity, historically, has been Evangelical Lutheran for the most part since the Protestant Reformation in the 1500's. The Swedish Lutheran Church is very similar to the Anglican or Episcopal Church in that it has an episcopal form of government. The Swedish Lutheran Church also has a very dignified liturgy that preserves the historic order of the Mass, much like you might see in a "Evangelical Catholic" congregation in the Lutheran Church-Missouri Synod here in the United States. Unfortunately, at least since the middle of the last century, the Church of Sweden has been quite lukewarm theologically. Like most State Churches, it permits almost every conceivable kind of belief these days, and doesn't seem to hold its pastors to even historic Lutheran beliefs much anymore. Theologically, it is very similar to the Episcopal Church in the United States, in that it is very progressive. It has ordained women to the priesthood since the 1960's. It has no problem with the gay agenda and has recently appointed a lesbian as the Bishop of Stockholm. The Church of Sweden has also recently approved of same sex marriages. Nevertheless, there are still pockets of traditionalists and conservatives in the Church of Sweden, although they are not in positions of authority. In terms of liturgical services, the Church of Sweden is still very traditional. Worship is usually accompanied by a pipe organ and the churches closely follow the liturgy and rarely deviate from it. The liturgy of the Church of Sweden is a modified form of the Roman Catholic Mass.
Here are a few examples of services:
1. A Selection from the Swedish Eucharist: http://youtu.be/cx2N-J2ujuk
2. The First Sunday of Advent from Falu Cathedral: http://youtu.be/wzYdPHAjZWI
3. Vespers from Uppsala Cathedral on the Feast of the Beheading of St. John the Baptist: http://youtu.be/MiTHGXtmE9U
These videos should give you a feel for the Church of Sweden.