Calculating peaks in histograms or density functions

Finding Peaks in density functions is, as already given in the comments, related to Finding local maxima and minima where you can find more solutions. The answer of chthonicdaemon is close to the peak, but each diff is reducing the vector length by one.

#Create Dataset
x <- c(1,1,4,4,9)

#Estimate Density
d <- density(x)

#Two ways to get highest Peak
d$x[d$y==max(d$y)]  #Gives you all highest Peaks
d$x[which.max(d$y)] #Gives you the first highest Peak

#3 ways to get all Peaks
d$x[c(F, diff(diff(d$y)>=0)<0)] #This detects also a plateau
d$x[c(F, diff(sign(diff(d$y)))<0)]
d$x[which(diff(sign(diff(d$y)))<0)+1]

#In case you also want the height of the peaks
data.frame(d[c("x", "y")])[c(F, diff(diff(d$y)>=0)<0),]

#In case you need a higher "precision"
d <- density(x, n=1e4)

If your y values are smooth (like in your sample plot), this should find the peaks pretty repeatably:

peakx <- x[which(diff(sign(diff(y)))==-2)]