matplotlib get ylim values

 ymin, ymax = axes.get_ylim()

If you are using the plt api directly, you can avoid calls to axes altogether:

def myplotfunction(title, values, errors, plot_file_name):

    # plot errorbars
    indices = range(0, len(values))
    fig = plt.figure()
    plt.errorbar(tuple(indices), tuple(values), tuple(errors), marker='.')

    plt.ylim([-0.5, len(values) - 0.5])
    plt.xlabel('My x-axis title')
    plt.ylabel('My y-axis title')

    # title
    plt.title(title)

    # save as file
    plt.savefig(plot_file_name)

   # close figure
    plt.close(fig)

Leveraging from the good answers above and assuming you were only using plt as in

import matplotlib.pyplot as plt

then you can get all four plot limits using plt.axis() as in the following example.

import matplotlib.pyplot as plt

x = [1, 2, 3, 4, 5, 6, 7, 8]  # fake data
y = [1, 2, 3, 4, 3, 2, 5, 6]

plt.plot(x, y, 'k')

xmin, xmax, ymin, ymax = plt.axis()

s = 'xmin = ' + str(round(xmin, 2)) + ', ' + \
    'xmax = ' + str(xmax) + '\n' + \
    'ymin = ' + str(ymin) + ', ' + \
    'ymax = ' + str(ymax) + ' '

plt.annotate(s, (1, 5))

plt.show()

The above code should produce the following output plot.

Just use axes.get_ylim(), it is very similar to set_ylim. From the docs:

get_ylim()

Get the y-axis range [bottom, top]