There's the World of the Living, the Dangai, Soul Society, Royal Dimension, Hell, Hueco Mundo, whatever dimension Caja Negación sends you to,... So, in total, there are 7 dimensions. 8 if you count the Schatten Bereich, a dimension inside of Soul Society. Also, Garganta's make you travel through the void between dimensions, so if you want to count that as well...