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

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.

   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

Using the data.table_1.9.5, this can be done without the melt as it can handle multiple value.var columns. You can install it from here

 library(data.table)
 dcast(setDT(my.df), ID~TIME, value.var=c('X', 'Y'))
 #   ID 1_X 2_X 3_X 4_X 5_X 1_Y 2_Y 3_Y 4_Y 5_Y
 #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

Note -Sept 2019: within tidyr, the gather()+spread() approach (described in this answer) has more or less been replaced by the pivot_wider() approach (described in `this newer tidyr answer). For current info about the transition, see the pivoting vignette.

Here's a solution with the tidyr package, which has essentially replaced reshape and reshape2. As with those two packages, the strategy it to make the dataset longer first, and then wider.

library(magrittr); requireNamespace("tidyr"); requireNamespace("dplyr")
my.df %>%
  tidyr::gather(key=variable, value=value, c(X, Y)) %>%   # Make it even longer.
  dplyr::mutate(                                          # Create the spread key.
    time_by_variable   = paste0(variable, "_", TIME)
  ) %>%
  dplyr::select(ID, time_by_variable, value) %>%          # Retain these three.
  tidyr::spread(key=time_by_variable, value=value)        # Spread/widen.

After the tidyr::gather() call, the intermediate dataset is:

ID TIME variable value
1   A    1        X     1
2   B    1        X     2
3   C    1        X     3
...
28  A    5        Y    28
29  B    5        Y    29
30  C    5        Y    30

The eventual result is:

  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

tidyr::unite() is an alternative, suggested by @JWilliman. This is functionally equivalent to the dplyr::mutate() and dplyr::select() combination above, when the remove parameter is true (which is the default).

If you're not accustomed to this type of manipulation, the tidyr::unite() may be a small obstacle because it's one more function you have to learn & remember. However, it's benefits include (a) more concise code (ie, four lines are replaced by one) and (b) fewer places to repeat variable names (ie, you don't have to repeat/modify variables in the dplyr::select() clause).

my.df %>%
  tidyr::gather(key=variable, value=value, c(X, Y)) %>%           # Make it even longer.
  tidyr::unite("time_by_variable", variable, TIME, remove=T) %>%  # Create the spread key `time_by_variable` while simultaneously dropping `variable` and `TIME`.
  tidyr::spread(key=time_by_variable, value=value)                # Spread/widen.

The pivot_wider() function is tidyr's 2nd generation approach (released in tidyr 1.0.0).

library(magrittr); requireNamespace("tidyr");

my.df %>%
  tidyr::pivot_wider(
    names_from  = c(TIME), # Can accommodate more variables, if needed.
    values_from = c(X, Y)
  )

Result:

# A tibble: 3 x 11
  ID      X_1   X_2   X_3   X_4   X_5   Y_1   Y_2   Y_3   Y_4   Y_5
  <fct> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int>
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

This is probably preferable to the previous tidyr approach (that uses a combination of gather() and spread()).

More capabilities are described in the pivoting vignette. This example is particularly concise because your desired specifications match the defaults of the id_cols and names_sep.