You can use melt
:
print pd.melt(df,id_vars=['state'],var_name="year", value_name="unemployment")
state year unemployment
0 AL 2004 5.7
1 AK 2004 7.5
2 AZ 2004 5.0
3 AR 2004 5.7
4 CA 2004 6.2
5 AL 2005 4.5
6 AK 2005 6.9
7 AZ 2005 4.7
8 AR 2005 5.2
9 CA 2005 5.4
10 AL 2006 4.0
11 AK 2006 6.6
12 AZ 2006 4.2
13 AR 2006 5.2
14 CA 2006 4.9
15 AL 2007 4.0
16 AK 2007 6.3
17 AZ 2007 3.9
18 AR 2007 5.3
19 CA 2007 5.4
20 AL 2008 5.7
21 AK 2008 6.7
22 AZ 2008 6.2
23 AR 2008 5.5
24 CA 2008 7.3
25 AL 2009 11.0
26 AK 2009 7.7
27 AZ 2009 9.9
28 AR 2009 7.8
29 CA 2009 11.2
30 AL 2010 10.5
31 AK 2010 7.9
32 AZ 2010 10.4
33 AR 2010 8.2
34 CA 2010 12.2
35 AL 2011 9.6
36 AK 2011 7.6
37 AZ 2011 9.5
38 AR 2011 8.3
39 CA 2011 11.7
40 AL 2012 8.0
41 AK 2012 7.1
42 AZ 2012 8.3
43 AR 2012 7.6
44 CA 2012 10.4
45 AL 2013 7.2
46 AK 2013 6.9
47 AZ 2013 7.7
48 AR 2013 7.3
49 CA 2013 8.9
50 AL 2014 6.8
51 AK 2014 6.9
52 AZ 2014 6.8
53 AR 2014 6.1
54 CA 2014 7.5
55 AL 2015 6.1
56 AK 2015 6.5
57 AZ 2015 6.1
58 AR 2015 5.2
59 CA 2015 6.2