You could use the reshape2-package:
# load package
> require(reshape2)
# create an example matrix
> mdat <- matrix(c(1,2,3, 11,12,13), nrow = 2, ncol=3, byrow=TRUE,
+ dimnames = list(c("row1", "row2"),
+ c("C.1", "C.2", "C.3")))
> mdat
C.1 C.2 C.3
row1 1 2 3
row2 11 12 13
# bring matrix to long format using melt()
> melt(mdat)
Var1 Var2 value
1 row1 C.1 1
2 row2 C.1 11
3 row1 C.2 2
4 row2 C.2 12
5 row1 C.3 3
6 row2 C.3 13