Plot labels at ends of lines

To use Baptiste's idea, you need to turn off clipping. But when you do, you get garbage. In addition, you need to suppress the legend, and, for geom_text, select Capex for 2014, and increase the margin to give room for the labels. (Or you can adjust the hjust parameter to move the labels inside the plot panel.) Something like this:

library(ggplot2)
library(grid)

p = ggplot(temp.dat) + 
  geom_line(aes(x = Year, y = Capex, group = State, colour = State)) + 
  geom_text(data = subset(temp.dat, Year == "2014"), aes(label = State, colour = State, x = Inf, y = Capex), hjust = -.1) +
  scale_colour_discrete(guide = 'none')  +    
  theme(plot.margin = unit(c(1,3,1,1), "lines")) 

# Code to turn off clipping
gt <- ggplotGrob(p)
gt$layout$clip[gt$layout$name == "panel"] <- "off"
grid.draw(gt)

But, this is the sort of plot that is perfect for directlabels.

library(ggplot2)
library(directlabels)

ggplot(temp.dat, aes(x = Year, y = Capex, group = State, colour = State)) + 
  geom_line() +
  scale_colour_discrete(guide = 'none') +
  scale_x_discrete(expand=c(0, 1)) +
  geom_dl(aes(label = State), method = list(dl.combine("first.points", "last.points")), cex = 0.8) 

Edit To increase the space between the end point and the labels:

ggplot(temp.dat, aes(x = Year, y = Capex, group = State, colour = State)) + 
  geom_line() +
  scale_colour_discrete(guide = 'none') +
  scale_x_discrete(expand=c(0, 1)) +
  geom_dl(aes(label = State), method = list(dl.trans(x = x + 0.2), "last.points", cex = 0.8)) +
  geom_dl(aes(label = State), method = list(dl.trans(x = x - 0.2), "first.points", cex = 0.8)) 

I provide another answer for weary ggplot folk.

This solution's principle can be applied quite generally.

Plot_df <- 
  temp.dat %>% mutate_if(is.factor, as.character) %>%  # Who has time for factors..
  mutate(Year = as.numeric(Year))

And now, we can subset our data

ggplot() + 
geom_line(data = Plot_df, aes(Year, Capex, color = State)) +
geom_text(data = Plot_df %>% filter(Year == last(Year)), aes(label = State, 
                                                           x = Year + 0.5, 
                                                           y = Capex, 
                                                           color = State)) + 
          guides(color = FALSE) + theme_bw() + 
          scale_x_continuous(breaks = scales::pretty_breaks(10))

The last pretty_breaks part is just to fix the axis below.

Not sure if it is the best way, but you could try the following (play a bit with xlim for correctly setting the limits):

library(dplyr)
lab <- tapply(temp.dat$Capex, temp.dat$State, last)
ggplot(temp.dat) + 
    geom_line(aes(x = Year, y = Capex, group = State, colour = State)) +
    scale_color_discrete(guide = FALSE) +
    geom_text(aes(label = names(lab), x = 12, colour = names(lab), y = c(lab), hjust = -.02))

A newer solution is to use ggrepel:

library(ggplot2)
library(ggrepel)
library(dplyr)

temp.dat %>%
  mutate(label = if_else(Year == max(Year), as.character(State), NA_character_)) %>%
  ggplot(aes(x = Year, y = Capex, group = State, colour = State)) + 
  geom_line() + 
  geom_label_repel(aes(label = label),
                  nudge_x = 1,
                  na.rm = TRUE)