library(dplyr)

df <- data.frame(grp_A = c(13, NA, NA, NA, NA, 20, NA),
             grp_B = c(NA, 59, 66, NA, NA, NA, NA),
             grp_C = c(NA, NA, NA, 23, 42, NA, NA))

df$value <- apply(select(df, grp_A, grp_B, grp_C), 1,
              function(x) x[!is.na(x)])