How to create thiessen polygons from points using R packages?

You haven't given us access to your data, but here's an example for points representing cities of the world, using an approach described by Carson Farmer on his blog. Hopefully it'll get you started...

# Carson's Voronoi polygons function
voronoipolygons <- function(x) {
  require(deldir)
  require(sp)
  if (.hasSlot(x, 'coords')) {
    crds <- x@coords  
  } else crds <- x
  z <- deldir(crds[,1], crds[,2])
  w <- tile.list(z)
  polys <- vector(mode='list', length=length(w))
  for (i in seq(along=polys)) {
    pcrds <- cbind(w[[i]]$x, w[[i]]$y)
    pcrds <- rbind(pcrds, pcrds[1,])
    polys[[i]] <- Polygons(list(Polygon(pcrds)), ID=as.character(i))
  }
  SP <- SpatialPolygons(polys)
  voronoi <- SpatialPolygonsDataFrame(SP, data=data.frame(x=crds[,1],
    y=crds[,2], row.names=sapply(slot(SP, 'polygons'), 
    function(x) slot(x, 'ID'))))
}

Example 1: Input is a SpatialPointsDataFrame:

# Read in a point shapefile to be converted to a Voronoi diagram
library(rgdal)
dsn <- system.file("vectors", package = "rgdal")[1]
cities <- readOGR(dsn=dsn, layer="cities")

v <- voronoipolygons(cities)

plot(v)

Example 2: Input is vectors of x, y coordinates:

dat <- data.frame(x=runif(100), y=runif(100))
v2 <- voronoipolygons(dat)
plot(v2)

Same principle as shown by jbaums, but simpler code:

library(dismo)
library(rgdal)
cities <- shapefile(file.path(system.file("vectors", package = "rgdal")[1], "cities"))

v <- voronoi(cities)
plot(v)