Concatenate column values in Pandas DataFrame with "NaN" values

I don't think your problem is trivial. However, here is a workaround using numpy vectorization :

In [49]: def concat(*args):
    ...:     strs = [str(arg) for arg in args if not pd.isnull(arg)]
    ...:     return ','.join(strs) if strs else np.nan
    ...: np_concat = np.vectorize(concat)
    ...: 

In [50]: np_concat(df['col2'], df['col3'])
Out[50]: 
array(['p1,A', 'p2,B', 'p1,C', 'D', 'p2,E', 'F'], 
      dtype='|S64')

In [51]: df['concatenated'] = np_concat(df['col2'], df['col3'])

In [52]: df
Out[52]: 
  col1 col2 col3 concatenated
0    1   p1    A         p1,A
1    1   p2    B         p2,B
2    2   p1    C         p1,C
3    2  NaN    D            D
4    3   p2    E         p2,E
5    3  NaN    F            F

[6 rows x 4 columns]

You could first replace NaNs with empty strings, for the whole dataframe or the column(s) you desire.

In [6]: df = df.fillna('')

In [7]: df['concatenated'] = df['col2'] +','+ df['col3']

In [8]: df
Out[8]:
  col1 col2 col3 concatenated
0    1   p1    A         p1,A
1    1   p2    B         p2,B
2    2   p1    C         p1,C
3    2         D           ,D
4    3   p2    E         p2,E
5    3         F           ,F