There are many meanings associated to fire, which are primarily transformation, destruction, passion, knowledge, and warning. It has been used in religious rites (the smoke wafting towards heaven), and is believed to make wishes come true.
Fire is feared and respected due to its destructive ability which makes it ultimately powerful. In Christianity, it is also the symbol of God, but at the same time, it is the symbol of Hell as well. It also symbolizes temptation and sin.
In Greece, fire is the symbol of hope. It is connected to the legend of Prometheus, who stole the fire from the gods to give it to mankind, though he was cruelly scourged for his act.
A notable creature that is strong connection with fire is the Phoenix, which can regenerate after dying in flames. So it is a common tattoo theme, too.
Other than phoenixes, flames can be associated with many tattoo designs. It looks good in a destructive image - like when flames engulf buildings, but in a positive connotation also, like fire surrounding a heart, which means passion and love.