I have two vectors, one with values and one with class labels like 1,2,3 etc.

I would like to plot all the points that belong to class 1 in red, to class 2 in blue, to class 3 in green etc. How can I do that?

The accepted answer has it spot on, but if you might want to specify which class label should be assigned to a specific color or label you could do the following. I did a little label gymnastics with the colorbar, but making the plot itself reduces to a nice one-liner. This works great for plotting the results from classifications done with sklearn. Each label matches a (x,y) coordinate.

import matplotlib
import matplotlib.pyplot as plt
import numpy as np

x = [4,8,12,16,1,4,9,16]
y = [1,4,9,16,4,8,12,3]
label = [0,1,2,3,0,1,2,3]
colors = ['red','green','blue','purple']

fig = plt.figure(figsize=(8,8))
plt.scatter(x, y, c=label, cmap=matplotlib.colors.ListedColormap(colors))

cb = plt.colorbar()
loc = np.arange(0,max(label),max(label)/float(len(colors)))
cb.set_ticks(loc)
cb.set_ticklabels(colors)

Using a slightly modified version of this answer, one can generalise the above for N colors as follows:

import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt

N = 23 # Number of labels

# setup the plot
fig, ax = plt.subplots(1,1, figsize=(6,6))
# define the data
x = np.random.rand(1000)
y = np.random.rand(1000)
tag = np.random.randint(0,N,1000) # Tag each point with a corresponding label    

# define the colormap
cmap = plt.cm.jet
# extract all colors from the .jet map
cmaplist = [cmap(i) for i in range(cmap.N)]
# create the new map
cmap = cmap.from_list('Custom cmap', cmaplist, cmap.N)

# define the bins and normalize
bounds = np.linspace(0,N,N+1)
norm = mpl.colors.BoundaryNorm(bounds, cmap.N)

# make the scatter
scat = ax.scatter(x,y,c=tag,s=np.random.randint(100,500,N),cmap=cmap,     norm=norm)
# create the colorbar
cb = plt.colorbar(scat, spacing='proportional',ticks=bounds)
cb.set_label('Custom cbar')
ax.set_title('Discrete color mappings')
plt.show()

Which gives: