How to add a new column to an existing DataFrame?

I have the following indexed DataFrame with named columns and rows not- continuous numbers:

          a         b         c         d
2  0.671399  0.101208 -0.181532  0.241273
3  0.446172 -0.243316  0.051767  1.577318
5  0.614758  0.075793 -0.451460 -0.012493

I would like to add a new column, 'e', to the existing data frame and do not want to change anything in the data frame (i.e., the new column always has the same length as the DataFrame).

0   -0.335485
1   -1.166658
2   -0.385571
dtype: float64

How can I add column e to the above example?

Edit 2017

As indicated in the comments and by @Alexander, currently the best method to add the values of a Series as a new column of a DataFrame could be using assign:

df1 = df1.assign(e=pd.Series(np.random.randn(sLength)).values)

Edit 2015
Some reported getting the SettingWithCopyWarning with this code.
However, the code still runs perfectly with the current pandas version 0.16.1.

>>> sLength = len(df1['a'])
>>> df1
          a         b         c         d
6 -0.269221 -0.026476  0.997517  1.294385
8  0.917438  0.847941  0.034235 -0.448948

>>> df1['e'] = pd.Series(np.random.randn(sLength), index=df1.index)
>>> df1
          a         b         c         d         e
6 -0.269221 -0.026476  0.997517  1.294385  1.757167
8  0.917438  0.847941  0.034235 -0.448948  2.228131

>>> pd.version.short_version
'0.16.1'

The SettingWithCopyWarning aims to inform of a possibly invalid assignment on a copy of the Dataframe. It doesn't necessarily say you did it wrong (it can trigger false positives) but from 0.13.0 it let you know there are more adequate methods for the same purpose. Then, if you get the warning, just follow its advise: Try using .loc[row_index,col_indexer] = value instead

>>> df1.loc[:,'f'] = pd.Series(np.random.randn(sLength), index=df1.index)
>>> df1
          a         b         c         d         e         f
6 -0.269221 -0.026476  0.997517  1.294385  1.757167 -0.050927
8  0.917438  0.847941  0.034235 -0.448948  2.228131  0.006109
>>> 

In fact, this is currently the more efficient method as described in pandas docs

Original answer:

Use the original df1 indexes to create the series:

df1['e'] = pd.Series(np.random.randn(sLength), index=df1.index)

This is the simple way of adding a new column: df['e'] = e