A ggplot2 version of this article. Data setup:

# set up the data
df <- data.frame(Circulatory=c(32,26,19,16,14,13,11,11),
                 Mental=c(11,11,18,24,23,24,26,23),
                 Musculoskeletal=c(17,18,13,16,12,18,20,26),
                 Cancer=c(10,15,15,14,16,16,14,14))

df$year <- seq(1975,2010,by=5)

Now the plot, using tidyr and ggplot2:

library(tidyr)
library(ggplot2)

gathered <- gather(df, cause, percentage, -year)
crossed <- crossing(gathered, highlight = unique(gathered$cause))

ggplot(crossed, aes(year, percentage, group = cause,
                    color = highlight == cause)) +
  geom_line(show.legend = FALSE) +
  facet_wrap(~ highlight) +
  scale_color_manual(values = c("gray", "darkblue")) +
  theme_minimal()

For the curious: this works by quadrupling the dataset, once for each highlight:

head(crossed)
##   year       cause percentage       highlight
## 1 1975 Circulatory         32          Cancer
## 2 1975 Circulatory         32     Circulatory
## 3 1975 Circulatory         32          Mental
## 4 1975 Circulatory         32 Musculoskeletal
## 5 1980 Circulatory         26          Cancer
## 6 1980 Circulatory         26     Circulatory