date <- seq(as.Date("2012-09-01"), Sys.Date(), 1)
id <- rep(c("a","b","c","d"), 8)
bdate <- seq(as.Date("2012-08-01"), as.Date("2012-11-01"), 1)[sample(1:32, 32)]

# The end date should be random but greater than the begin date. However, I set it to 15 days later for simplicity.
edate <- bdate + 15

value <- seq(1, 1000, 1)[sample(1:1000, 32)]
dfa <- data.frame(id, value, bdate, edate)
names(dfa) <- c("ID", "Value", "Begin.Date", "End.Date")

Date        a   b   c
2012-08-01  XXX YYY ZZZ
2012-08-02  XXX YYY ZZZ
2012-08-03  XXX YYY ZZZ

# Create additional data frame
dfb <- data.frame(seq(as.Date("2012-08-01"), as.Date("2012-11-01"), 1))
names(dfb)[1] <- "Date"

# Variable for unique IDs
nid <- unique(dfa$ID)

# Number of total IDs
tid <- length(nid)

for (i in c(1:tid))
{
sums <- vapply(dfb$Date, function(x)
{
temp <- subset(dfa, dfa$ID == nid[i])
temp <- subset(temp, temp$Begin.Date < x & temp$End.Date > x)
res <- sum(temp$Value)
res
}, FUN.VALUE = 0.1
)
dfb[1+i] <- sums
}

# Change column names to ID
names(dfb) <- c("Date", as.character(nid))

mydate <- as.Date("2012-08-25")  # take Aug 25, 2012 as an example
ind <- (dfa$Begin.Date <= mydate) & (dfa$End.Date >= mydate)
temp <- subset(dfa, ind)
out <- table(temp$ID)

library("plyr")
library("reshape2")

earliest.date <- as.Date("2007-01-01")
latest.date <- as.Date("2012-11-01")

dfa.long <- adply(dfa, 1, function(DF) {
  if(DF$End.Date >= earliest.date & DF$Begin.Date <= latest.date) {
    data.frame(Date=seq(max(DF$Begin.Date, earliest.date),
                        min(DF$End.Date, latest.date),
                        1))
  }
})

dfb <- ddply(dfa.long, .(Date, ID), summarise, sum=sum(Value))
dfb <- dcast(dfb, Date~ID, value.var="sum", fill=0)