Label points in geom_point

Use geom_text , with aes label. You can play with hjust, vjust to adjust text position.

ggplot(nba, aes(x= MIN, y= PTS, colour="green", label=Name))+
  geom_point() +geom_text(hjust=0, vjust=0)

EDIT: Label only values above a certain threshold:

  ggplot(nba, aes(x= MIN, y= PTS, colour="green", label=Name))+
  geom_point() +
  geom_text(aes(label=ifelse(PTS>24,as.character(Name),'')),hjust=0,vjust=0)

The ggrepel package works great for repelling overlapping text labels away from each other. You can use either geom_label_repel() (draws rectangles around the text) or geom_text_repel() functions.

library(ggplot2)
library(ggrepel)

nba <- read.csv("http://datasets.flowingdata.com/ppg2008.csv", sep = ",")

nbaplot <- ggplot(nba, aes(x= MIN, y = PTS)) + 
  geom_point(color = "blue", size = 3)

### geom_label_repel
nbaplot + 
  geom_label_repel(aes(label = Name),
                  box.padding   = 0.35, 
                  point.padding = 0.5,
                  segment.color = 'grey50') +
  theme_classic()

### geom_text_repel
# only label players with PTS > 25 or < 18
# align text vertically with nudge_y and allow the labels to 
# move horizontally with direction = "x"
ggplot(nba, aes(x= MIN, y = PTS, label = Name)) + 
  geom_point(color = dplyr::case_when(nba$PTS > 25 ~ "#1b9e77", 
                                      nba$PTS < 18 ~ "#d95f02",
                                      TRUE ~ "#7570b3"), 
             size = 3, alpha = 0.8) +
  geom_text_repel(data          = subset(nba, PTS > 25),
                  nudge_y       = 32 - subset(nba, PTS > 25)$PTS,
                  size          = 4,
                  box.padding   = 1.5,
                  point.padding = 0.5,
                  force         = 100,
                  segment.size  = 0.2,
                  segment.color = "grey50",
                  direction     = "x") +
  geom_label_repel(data         = subset(nba, PTS < 18),
                  nudge_y       = 16 - subset(nba, PTS < 18)$PTS,
                  size          = 4,
                  box.padding   = 0.5,
                  point.padding = 0.5,
                  force         = 100,
                  segment.size  = 0.2,
                  segment.color = "grey50",
                  direction     = "x") +
  scale_x_continuous(expand = expand_scale(mult = c(0.2, .2))) +
  scale_y_continuous(expand = expand_scale(mult = c(0.1, .1))) +
  theme_classic(base_size = 16)

Edit: To use ggrepel with lines, see this and this.

^{Created on 2019-05-01 by the reprex package (v0.2.0).}

Instead of using the ifelse as in the above example, one can also prefilter the data prior to labeling based on some threshold values, this saves a lot of work for the plotting device:

xlimit <- 36
ylimit <- 24
ggplot(myData)+geom_point(aes(myX,myY))+
    geom_label(data=myData[myData$myX > xlimit & myData$myY> ylimit,], aes(myX,myY,myLabel))