There is a general misconception that 'Gothic' culture is related to a particular religious persuasion, and 'Satanism' and 'devil worship' are phrases often bandied about. The truth is that, although Gothic art, music and literature does draw its influences from dark and macabre themes, religion actually has very little to do with Gothic culture.
Use of Satanic symbols
The main source of confusion is the use of what can be considered 'Satanic' symbols such as pentagrams, reversed crosses, and other occult imagery.
The first thing to point out is that not all occult practices have a 'Satanic' or nefarious intention: The use of the pentagram, for example, can be attributed to everything from Christianity (where it represented the 5 wounds of Jesus) and Wicca (or white magic), through to the Greek mathematician Pythagorus.
Goth versus other genres
Having said that, there are instances where Satanic symbols are used in things ranging from Gothic jewellery and clothing, as well as in the album-sleeve art of Gothic musicians.
Purist Goths would probably argue that the idea of 'Satanic' imagery was never popular with the original 'Goth' movement that emerged from the post-punk scene of the 1980s; and would point out that it has only been since the emergence of genres like death-metal, heavy-metal and thrash that Gothic elements have fused with other sub-cultures to create such confusion about what 'Goth' actually means.
Aesthetic Value
Another way to look at the presence of Satanic imagery in Goth art is in much the same way that we view vampire movies or horror movies in popular culture. Although we may all take some enjoyment from watching actors like Robert Pattinson (Twilight) or Brad Pitt and Tom Cruise (Interview with a Vampire) sink their teeth into the necks of unsuspecting victims and feast on their blood, we are unlikely to replicate the act whilst taking the dog for a walk.
In much the same way, although Goths may seem obsessed with death, the Devil, the living dead, and other gruesome themes, this is more for their aesthetic value than from any urge to replicate them in real life.
Goth attitudes to religion
One last point to make is that, although being a Goth doesn't categorically imply any particular view on religion, it isn't uncommon for people of any sub-culture to view institutions such as organized religion with some skepticism and even disdain.
This is largely due to Gothic culture being a form of counter-culture, where social norms such as religion and politics are often viewed in an antagonistic light purely because of their place in mainstream society.
This concept is also by no means unique to Goths, but is an idea that manifests itself in counter-cultures ranging from the Beat Generation of 1950s America through to the modern Russian literary and artistic counter-culture or Контркультура.