Margie Kieper
EF1
We're approaching the quietest time of the year as far as global TC activity. The longest periods have all started about a month from now, but a quiescent period could start earlier -- unless you believe the GFS long-term take on a possible subtropical storm around the Bahamas and Bermuda in a week. 
Here are the stats on the longest documented times between 1964 and 2004 with no active tropical cyclones, that I calculated in January, using the NHC and JTWC best tracks (at the time, JTWC best tracks for 2005 were not available):
quiescent days____quiescent period
31________________Apr 16, 84 to May 16, 84
30________________Apr 20, 85 to May 19, 85
21________________Apr 17, 88 to May 07, 88
18________________Apr 16, 04 to May 03, 04
17________________May 12, 75 to May 28, 75
17________________Apr 27, 78 to May 13, 78
16________________Mar 25, 90 to Apr 09, 90
15________________Jan 10, 04 to Jan 24, 04
14________________Apr 24, 72 to May 07, 72
13________________Apr 01, 74 to Apr 13, 74
12________________Dec 25, 74 to Jan 05, 75
12________________Apr 15, 65 to Apr 26, 65
12________________May 01, 69 to May 12, 69
12________________May 18, 78 to May 29, 78
12________________Dec 01, 78 to Dec 12, 78
12________________Dec 25, 85 to Jan 05, 86
12________________Dec 28, 90 to Jan 08, 91
12________________May 03, 92 to May 14, 92
11________________May 21, 92 to May 31, 92
11________________May 04, 99 to May 14, 99
11________________Jun 02, 78 to Jun 12, 78
11________________Nov 29, 69 to Dec 09, 69
11________________Mar 14, 76 to Mar 24, 76
10________________Jun 08, 75 to Jun 17, 75
10________________Mar 24, 84 to Apr 02, 84
10________________Jun 21, 69 to Jun 30, 69
10________________Oct 26, 65 to Nov 04, 65
10________________May 13, 72 to May 22, 72
10________________Mar 30, 97 to Apr 08, 97
quiescent days / num_of_occurances
31_____________1
30_____________1
21_____________1
18_____________1
17_____________2
16_____________1
15_____________1
14_____________1
13_____________1
12_____________8
11_____________5
10_____________6
_9_____________3
_8_____________9
_7_____________8
_6____________11
_5____________23
_4____________13
_3____________21
_2____________28
_1____________32

Here are the stats on the longest documented times between 1964 and 2004 with no active tropical cyclones, that I calculated in January, using the NHC and JTWC best tracks (at the time, JTWC best tracks for 2005 were not available):
quiescent days____quiescent period
31________________Apr 16, 84 to May 16, 84
30________________Apr 20, 85 to May 19, 85
21________________Apr 17, 88 to May 07, 88
18________________Apr 16, 04 to May 03, 04
17________________May 12, 75 to May 28, 75
17________________Apr 27, 78 to May 13, 78
16________________Mar 25, 90 to Apr 09, 90
15________________Jan 10, 04 to Jan 24, 04
14________________Apr 24, 72 to May 07, 72
13________________Apr 01, 74 to Apr 13, 74
12________________Dec 25, 74 to Jan 05, 75
12________________Apr 15, 65 to Apr 26, 65
12________________May 01, 69 to May 12, 69
12________________May 18, 78 to May 29, 78
12________________Dec 01, 78 to Dec 12, 78
12________________Dec 25, 85 to Jan 05, 86
12________________Dec 28, 90 to Jan 08, 91
12________________May 03, 92 to May 14, 92
11________________May 21, 92 to May 31, 92
11________________May 04, 99 to May 14, 99
11________________Jun 02, 78 to Jun 12, 78
11________________Nov 29, 69 to Dec 09, 69
11________________Mar 14, 76 to Mar 24, 76
10________________Jun 08, 75 to Jun 17, 75
10________________Mar 24, 84 to Apr 02, 84
10________________Jun 21, 69 to Jun 30, 69
10________________Oct 26, 65 to Nov 04, 65
10________________May 13, 72 to May 22, 72
10________________Mar 30, 97 to Apr 08, 97
quiescent days / num_of_occurances
31_____________1
30_____________1
21_____________1
18_____________1
17_____________2
16_____________1
15_____________1
14_____________1
13_____________1
12_____________8
11_____________5
10_____________6
_9_____________3
_8_____________9
_7_____________8
_6____________11
_5____________23
_4____________13
_3____________21
_2____________28
_1____________32