round a date in R to an arbitrary minute/hour level of precision

lubridate now has a more generic round_date() function.

lubridate::round_date(date, "5 mins")
lubridate::round_date(date, "2 hours")

lubridate already floors to the nearest atomic unit. To get floor to the nearest 15 minutes, which I think is what you want to do (not round), you just need to map into the correct range via findInterval and a defined set of breakpoints. Try this floor_time, which is functionally equivalent to floor_date, but allows you to specify a variable # of units for seconds, minutes or hours.

floor_time <- function(x, k = 1, unit = c("second", "minute", "hour", "day", 
                                          "week", "month", "year")) {
  require(lubridate)

  nmax <- NULL

  switch(unit, second = {nmax <- 60},
         minute = {nmax <- 60},
         hour = {nmax <- 24})

  cuts <- seq(from = 0, to = nmax - 1, by = k)
  new <- switch(unit, 
                second = update(x, seconds = cuts[findInterval(second(x), cuts)]), 
                minute = update(x, minutes = cuts[findInterval(minute(x), cuts)], 
                                seconds = 0), 
                hour = update(x, hours = cuts[findInterval(hour(x), cuts)], 
                              minutes = 0, seconds = 0), 
                day = update(x, hours = 0, minutes = 0, seconds = 0), 
                week = update(x, wdays = 1, hours = 0, minutes = 0, seconds = 0), 
                month = update(x, mdays = 1, hours = 0, minutes = 0, seconds = 0), 
                year = update(x, ydays = 1, hours = 0, minutes = 0, seconds = 0))

  new
}

A little late, and I don't have rep to comment, but as Selva mentioned, lubridate now has this functionality:

library(lubridate)
round_date(now(), '3 hours')
floor_date(now(), '3 hours')
ceiling_date(now(), '3 hours')

You can try this, still based on the lubridate library

library(lubridate)
round_minute<-function(x,precision){
  m<-minute(x)+second(x)/60
  m.r<- round(m/precision)*precision
  minute(x)<-m.r
  second(x)<-0
  x
}

round_minute(ymd_hms(c("2013-06-03 22:53:00","2013-05-03 12:18:00","2013-05-03 00:10:00")),15)

> "2013-06-03 23:00:00 UTC" "2013-05-03 12:15:00 UTC" "2013-05-03 00:15:00 UTC"

The code handle well all the tricky situations thanks to lubridate. Of course this function works only for precision expressed in minutes but you can easily extend it to other units, and even create a generic function if you really need it.