Convert data from long format to wide format with multiple measure columns

   reshape(my.df,
           idvar = "ID",
           timevar = "TIME",
           direction = "wide")

gives

  ID X.1 Y.1 X.2 Y.2 X.3 Y.3 X.4 Y.4 X.5 Y.5
1  A   1  16   4  19   7  22  10  25  13  28
2  B   2  17   5  20   8  23  11  26  14  29
3  C   3  18   6  21   9  24  12  27  15  30

In order to handle multiple variables like you want, you need to melt the data you have before casting it.

library("reshape2")

dcast(melt(my.df, id.vars=c("ID", "TIME")), ID~variable+TIME)

which gives

  ID X_1 X_2 X_3 X_4 X_5 Y_1 Y_2 Y_3 Y_4 Y_5
1  A   1   4   7  10  13  16  19  22  25  28
2  B   2   5   8  11  14  17  20  23  26  29
3  C   3   6   9  12  15  18  21  24  27  30

---

EDIT based on comment:

The data frame

num.id = 10 
num.time=10 
my.df <- data.frame(ID=rep(LETTERS[1:num.id], num.time), 
                    TIME=rep(1:num.time, each=num.id), 
                    X=1:(num.id*num.time), 
                    Y=(num.id*num.time)+1:(2*length(1:(num.id*num.time))))

gives a different result (all entries are 2) because the ID/TIME combination does not indicate a unique row. In fact, there are two rows with each ID/TIME combinations. reshape2 assumes a single value for each possible combination of the variables and will apply a summary function to create a single variable is there are multiple entries. That is why there is the warning

Aggregation function missing: defaulting to length

You can get something that works if you add another variable which breaks that redundancy.

my.df$cycle <- rep(1:2, each=num.id*num.time)
dcast(melt(my.df, id.vars=c("cycle", "ID", "TIME")), cycle+ID~variable+TIME)

This works because cycle/ID/time now uniquely defines a row in my.df.