To find out how many rosemary plants were planted, we need to determine how many types of herbs were planted in total. The neighbor's planted basil, thyme, rosemary, and oregano, which means there are 4 types of herbs.
Since they planted the same number of each herb and the total number of plants is 52, we can divide the total number of plants by the number of types of herbs:
\[ \text{Number of plants per type of herb} = \frac{52 \text{ plants}}{4 \text{ types}} = 13 \text{ plants} \]
So, there were 13 plants of each type of herb, including rosemary.
Therefore, the answer is 13 rosemary plants.