A side comment here for those using any of these answers. Juba's answer is great, as it's very selective if your variables are either numberic or character strings. If however, you have a combination (e.g. a1, b1, a2, b2) etc. It will not convert the characters properly.
As @Trenton Hoffman notes,
library(dplyr)
df <- mutate_each(df, funs(toupper))
affects both character and factor classes and works for "mixed variables"; e.g. if your variable contains both a character and a numberic value (e.g. a1) both will be converted to a factor. Overall this isn't too much of a concern, but if you end up wanting match data.frames for example
df3 <- df1[df1$v1 %in% df2$v1,]
where df1 has been has been converted and df2 contains a non-converted data.frame or similar, this may cause some problems. The work around is that you briefly have to run
df2 <- df2 %>% mutate_each(funs(toupper), v1)
#or
df2 <- df2 %>% mutate_each(df2, funs(toupper))
#and then
df3 <- df1[df1$v1 %in% df2$v1,]
If you work with genomic data, this is when knowing this can come in handy.