Use merge, which is an inner join by default:

pd.merge(df1, df2, left_index=True, right_index=True)

Or join, which is a left join by default:

df1.join(df2)

Or concat), which is an outer join by default:

pd.concat([df1, df2], axis=1)

Samples:

df1 = pd.DataFrame({'a':range(6),
                    'b':[5,3,6,9,2,4]}, index=list('abcdef'))

print (df1)
   a  b
a  0  5
b  1  3
c  2  6
d  3  9
e  4  2
f  5  4

df2 = pd.DataFrame({'c':range(4),
                    'd':[10,20,30, 40]}, index=list('abhi'))

print (df2)
   c   d
a  0  10
b  1  20
h  2  30
i  3  40

# Default inner join
df3 = pd.merge(df1, df2, left_index=True, right_index=True)
print (df3)
   a  b  c   d
a  0  5  0  10
b  1  3  1  20

# Default left join
df4 = df1.join(df2)
print (df4)
   a  b    c     d
a  0  5  0.0  10.0
b  1  3  1.0  20.0
c  2  6  NaN   NaN
d  3  9  NaN   NaN
e  4  2  NaN   NaN
f  5  4  NaN   NaN

# Default outer join
df5 = pd.concat([df1, df2], axis=1)
print (df5)
     a    b    c     d
a  0.0  5.0  0.0  10.0
b  1.0  3.0  1.0  20.0
c  2.0  6.0  NaN   NaN
d  3.0  9.0  NaN   NaN
e  4.0  2.0  NaN   NaN
f  5.0  4.0  NaN   NaN
h  NaN  NaN  2.0  30.0
i  NaN  NaN  3.0  40.0

You can use concat([df1, df2, ...], axis=1) in order to concatenate two or more DFs aligned by indexes:

pd.concat([df1, df2, df3, ...], axis=1)

Or merge for concatenating by custom fields / indexes:

# join by _common_ columns: `col1`, `col3`
pd.merge(df1, df2, on=['col1','col3'])

# join by: `df1.col1 == df2.index`
pd.merge(df1, df2, left_on='col1' right_index=True)

or join for joining by index:

 df1.join(df2)