Adding y=x to a matplotlib scatter plot if I haven't kept track of all the data points that went in

You don't need to know anything about your data per se. You can get away with what your matplotlib Axes object will tell you about the data.

See below:

import numpy as np
import matplotlib.pyplot as plt

# random data 
N = 37
x = np.random.normal(loc=3.5, scale=1.25, size=N)
y = np.random.normal(loc=3.4, scale=1.5, size=N)
c = x**2 + y**2

# now sort it just to make it look like it's related
x.sort()
y.sort()

fig, ax = plt.subplots()
ax.scatter(x, y, s=25, c=c, cmap=plt.cm.coolwarm, zorder=10)

Here's the good part:

lims = [
    np.min([ax.get_xlim(), ax.get_ylim()]),  # min of both axes
    np.max([ax.get_xlim(), ax.get_ylim()]),  # max of both axes
]

# now plot both limits against eachother
ax.plot(lims, lims, 'k-', alpha=0.75, zorder=0)
ax.set_aspect('equal')
ax.set_xlim(lims)
ax.set_ylim(lims)
fig.savefig('/Users/paul/Desktop/so.png', dpi=300)

Et voilà

In one line:

ax.plot([0,1],[0,1], transform=ax.transAxes)

No need to modify the xlim or ylim.

If you set scalex and scaley to False, it saves a bit of bookkeeping. This is what I have been using lately to overlay y=x:

xpoints = ypoints = plt.xlim()
plt.plot(xpoints, ypoints, linestyle='--', color='k', lw=3, scalex=False, scaley=False)

or if you've got an axis:

xpoints = ypoints = ax.get_xlim()
ax.plot(xpoints, ypoints, linestyle='--', color='k', lw=3, scalex=False, scaley=False)

Of course, this won't give you a square aspect ratio. If you care about that, go with Paul H's solution.