aggregate(paste(ID , Date) ~ ID + Date, data = df, FUN = length)

library(dplyr)
df %>%  group_by(ID, Date) %>% summarise(PurchaseCount = n())
df %>% group_by(ID, Date) %>% tally(name="PurchaseCount")
df %>% group_by(ID, Date) %>% count(name="PurchaseCount")
df %>% group_by(ID, Date) %>% add_tally(name="PurchaseCount")
df %>% group_by(ID, Date) %>% add_count(name="PurchaseCount")

library(data.table)
setDT(df)[, PurchaseCount:=.N, by = list(ID, Date)]

library(sqldf)
sqldf("SELECT ID, Date, COUNT(*) as PurchaseCount
       FROM df
       GROUP BY Date, ID")