Using dplyr:
library(dplyr)
# exclude ID column then get mean
DF %>%
transmute(ID,
Mean = rowMeans(select(., -ID)))
Or
# select the columns to include in mean
DF %>%
transmute(ID,
Mean = rowMeans(select(., C1:C3)))
# ID Mean
# 1 A 3.666667
# 2 B 4.333333
# 3 C 3.333333
# 4 D 4.666667
# 5 E 4.333333