# Initialize data in row format in first data fram:
v1<-c("A",1,1.3)
v2<-c("A",2,1.8)
v3<-c("A",3,2.4)
v4<-c("B",1,0.8)
v5<-c("B",3,1.7)
first_DF<-data.frame(matrix(c(v1,v2,v3,v4,v5),ncol=3, nrow=5,byrow=TRUE,dimnames=list(NULL,c("Individual","DayAlive","Length"))), stringsAsFactors=FALSE)

# Convert to column format in second data frame:
individual_IDs<-unique(first_DF$"Individual")
days_alive<-unique(first_DF$"DayAlive")

# Initialize second DF by subsetting a single row for each individual from the first DF
second_DF<-data.frame(first_DF[which(first_DF$"Individual" %in% individual_IDs & first_DF$"DayAlive" %in% 1),1], stringsAsFactors=FALSE)
names(second_DF)<-"Individual"
initial_DF_width<-dim(second_DF)[2]

# Move 'Length' data into the columns as each 'day alive' column is created:
for(i in 1:length(days_alive)){
  current_day<-days_alive[i]
  second_DF<-cbind(second_DF,matrix(ncol=1, nrow=nrow(second_DF),dimnames=list(NULL,paste("Day ",current_day," Length"))))

  for(j in 1:length(individual_IDs)){
    current_individualID<-individual_IDs[j]
    length<-first_DF[which(first_DF$"Individual" %in% current_individualID & first_DF$"DayAlive" %in% current_day),"Length"]
    second_DF[j,i+initial_DF_width]<-length
  }
}

library('reshape2')

dcast(first_DF, Individual ~ DayAlive)
#   Individual   1    2   3
# 1          A 1.3  1.8 2.4
# 2          B 0.8 <NA> 1.7

for(i in 1:length(days_alive)){
  current_day<-days_alive[i]
  second_DF<-cbind(second_DF,matrix(ncol=1, nrow=nrow(second_DF),dimnames=list(NULL,paste("Day ",current_day," Length"))))

  for(j in 1:length(individual_IDs)){
    current_individualID<-individual_IDs[j]

    # I changed "length" to "length2" to avoid confusion with the
    # function length(). You also don't need which() here.
    length2 <- first_DF[first_DF$Individual %in% current_individualID
                        & first_DF$DayAlive %in% current_day, "Length"]
    if (length(length2) > 0) {
      second_DF[j, i + initial_DF_width] <- length2
    } else {
      second_DF[j, i + initial_DF_width] <- NA
    }
  }
}