The Shulhan Aruch (Orah Haim 224:13) rules that, regarding all blessings that involve seeing different things (such as seeing a king, or the other phenomenadiscussed in Siman 224), one makes a blessing only once every thirty days. In other words, if one were to see a king several times in a week, for example, one would only recite the blessing when seeing him the first time or after thirtyfrom the time one saw the king last. The rationale is that a blessing is onlyrecited when one experiences a sense of newness when one sees something, and this is Halachically defined as being only once every thirty days. If, however, one were to see different kings even within thirty days, one would recite the blessing for each king.
Another blessing in this category of things that are seen is recited when onesees Jewish graves or a Jewish cemetery, and is discussed in the Gemara (Berachot 59a) and codified in the Shulhan Aruch (ibid:12). One common trend nowadays is for people to go on excursions to visit the graves of differentprominent rabbis, such as in Israel or Morocco. There is discussion as to whether, here too, a blessing should be recited each time one sees a differentgrave. Rabbi Avraham Azoulay (gloss to the Levush, § 224) quoting the Radbaz (Shu”t HaRadbaz, § 562), writes that if one should recite a new blessing for each new grave that one saw, even if it was within thirty days. Even though Rabbi Yaakov Hagiz (Hilchot Ketanot, vol. I, § 212) says that if one were to see more than one grave one would not repeat the blessing, the HIDA (Birke Yosef, § 224:5), also citing the Radbaz, rules that one would do so. Indeed, many Aharonim agree with this positon, including Rabbi Ovadia Yosef (Hazon Ovadia, Hilchot Berachot, pg. 417), and this appears to be the accepted Halacha. It should be noted that this refers to graves found in differentlocations; if one remains in the same cemetery, only one blessing is recited every thirty days.
On a Kabbalistic level, Rabbi Avraham Azoulay and the HIDA (Birke Yosef, § 7) explain that when one visits a grave one should place one’s left hand on the grave and recite a verse from Yeshayahu 58:11. This verse has fifteen words and when reciting it, one should have in mind the fifteen different joints of one’s hand.
When one sees the grave of a non-Jew one should recite the verse from Yirmiyahu 50:12.
Summary: If one visits the graves of different rabbis (or Jews in general) in different locations, one may recite a blessing for each grave. One blessing is recited within the same cemetery, however.