At this point of IPL7, Kings XI Punjab have won all 3 games(successive), and this is the seventh time in IPL history that they won =>3 successive games.
The record for SUCCESSIVE wins is 7. This is currently held by Royal ChallengersBangalore(2011) & Chennai Super Kings(2013) is 7!
Here is year wise list of successive wins for all teams that took part in IPL.
2008
3 successive wins: Kolkata.
4 successive wins: Punjab & Chennai.
5 successive wins : Punjab & Jaipur.
6 successive wins: Mumbai & Jaipur.
Jaipur won the IPL tournament
2009
3 successive wins: Delhi, Punjab, Bangalore & Jaipur.
4 successive wins: Hyderabad & Delhi.
5 successive wins: Bangalore & Chennai.
Hyderabad won the IPL tournament
2010
3 successive wins: Mumbai & Chennai.
4 successive wins: Delhi, Jaipur, Chennai & Bangalore.
5 successive wins : Hyderabad & Mumbai.
Chennai won the IPL tournament
2011
3 successive wins: Hyderabad, Punjab, Kolkata, Kochi, Mumbai, & Chennai.
4 successive wins: Punjab & Chennai.
7 successive wins: Bangalore!.
Chennai winning consecutive IPL tournament!.
2012
3 successive wins: Mumbai, Chennai, & twice by Bangalore!.
4 successive wins: Delhi & twice by Kolkata!.
Kolkata won the IPL tournament
2013
3 successive wins: Punjab, Mumbai & Bangalore.
4 successive wins: Jaipur.
5 successive wins : Mumbai.
7 successive wins: Chennai.
Mumbai won the IPL tournament