Instead of using the outrageously convoluted data structures required by ggplot2, you can use the native R functions:
tab<-read.delim(text="
Company 2011 2013
Company1 300 350
Company2 320 430
Company3 310 420
",as.is=TRUE,sep=" ",row.names=1)
tab<-t(tab)
plot(tab[,1],type="b",ylim=c(min(tab),max(tab)),col="red",lty=1,ylab="Value",lwd=2,xlab="Year",xaxt="n")
lines(tab[,2],type="b",col="black",lty=2,lwd=2)
lines(tab[,3],type="b",col="blue",lty=3,lwd=2)
grid()
legend("topleft",legend=colnames(tab),lty=c(1,2,3),col=c("red","black","blue"),bg="white",lwd=2)
axis(1,at=c(1:nrow(tab)),labels=rownames(tab))
