How can I spread repeated measures of multiple variables into wide format?

Using reshape2:

library(reshape2)
dcast(melt(dat), Person ~ Time + variable)

Produces:

Using Person, Time as id variables
  Person Post_Score1 Post_Score2 Post_Score3 Pre_Score1 Pre_Score2 Pre_Score3
1   greg          79          78        83.5         83         81       87.0
2  sally          82          81        86.5         75         74       79.5
3    sue          78          78        83.0         82         79       85.5

Edit: I'm updating this answer since pivot_wider has been around for a while now and addresses the issue in this question and comments. You can now do

pivot_wider(
    dat, 
    id_cols = 'Person', 
    names_from = 'Time', 
    values_from = c('Score1', 'Score2', 'Score3'), 
    names_glue = '{Time}.{.value}'
)

to get the desired result.

---

The original answer was

dat %>% 
  gather(temp, score, starts_with("Score")) %>% 
  unite(temp1, Time, temp, sep = ".") %>% 
  spread(temp1, score)