The Goth sub-culture is not actually associated with any religion, but is a genre of literature, music and fashion that takes inspiration from the dark, sombre, and macabre. In this context, perhaps it is the darker elements of Christianity that Goths find aesthetically interesting, or perhaps it is simply because the symbol of the cross has powerful connotations across various beliefs and cultures.
The Christian meaning of the cross
In Christianity, the cross represents the death by crucifixion of Jesus Christ and, as a symbol, it embodies the mental, physical and spiritual suffering that Jesus withstood. It is also a symbol of the sacrifice that Jesus made on behalf of mankind.
For some Christians, wearing a cross is a way of literally wearing their faith on their sleeve - when you believe so strongly in something, it makes sense to want to shout about it from the roof tops.
For others, wearing a cross can be a reminder of the loving nature of God, of the protection and guidance he offers, or for a number of other reasons.
Themes like spiritual suffering, sacrificing oneself for the sins of humanity, and having an unshakeable faith in a transcendent spirit are leitmotifs in Gothic art, literature and culture, and might also be good reasons for a Goth to wear a cross.
Gothic art and Christianity
Reading briefly about the history of art and architecture will reveal that Christianity and the term 'Gothic art' are not as far removed as you may think.
The term 'Gothic' is often used to refer to the various styles of art and architecture that emerged during the middle ages (or the dark ages). This style was used to adorn various cathedrals, churches and abbeys- with one notable example being the Notre Dame de Paris in Paris, France.
Later, a resurgence of Gothic themes and concepts was key to various 'neo-Gothic' works of the 19th century in both Victorian literature and art that often had, as its backdrop, a Christian medieval setting.
Modern Goth culture
The misconception that modern Gothic culture has anything to do with Satanism and the occult is an understandable one. People who are constantly dressed in black, and have a particular appreciation for death and the darker things in life are hardly going to give the impression of being God-fearing and pious. However, this doesn't necessarily imply any stance for or against a particular belief system and, in fact, there are a growing number of 'Christian-Goth' communities (like this one here) that are attempting to counteract the stereotype that Goths and Christians don't mix.