First non-null value per row from a list of Pandas columns

Fill the nans from the left with fillna, then get the leftmost column:

df.fillna(method='bfill', axis=1).iloc[:, 0]

This is a really messy way to do this, first use first_valid_index to get the valid columns, convert the returned series to a dataframe so we can call apply row-wise and use this to index back to original df:

In [160]:
def func(x):
    if x.values[0] is None:
        return None
    else:
        return df.loc[x.name, x.values[0]]
pd.DataFrame(df.apply(lambda x: x.first_valid_index(), axis=1)).apply(func,axis=1)
​
Out[160]:
0     1
1     3
2     4
3   NaN
dtype: float64

EDIT

A slightly cleaner way:

In [12]:
def func(x):
    if x.first_valid_index() is None:
        return None
    else:
        return x[x.first_valid_index()]
df.apply(func, axis=1)

Out[12]:
0     1
1     3
2     4
3   NaN
dtype: float64