There is only one exercise that has been shown in a lab setting to increase intelligence:
Dual n Back.
It is an exercise where you train your brain to keep several different 'chunks' of information in your short term memory at the time.
From Wikipedia:
In a 2008 research paper Jaeggi et al. claim that practicing a dual n-back task can increase fluid intelligence, as measured in several different standard tests...
In 2009, it was reported in Science that '14 hours of training over 5 weeks' led to measurable density changes for cortical dopamine neuroreceptors.[5] N-back - Wikipedia, the free encyclopedia
You can read the paper here:
Improving fluid intelligence with training on working memory — PNAS
And, most importantly, you can play it online here:
Dual N-Back Training for Intelligence
I've been playing it a fair bit lately, and it is fascinating. What intrigues me the most is that I keep on getting it right when I think I have lost it and am only "guessing". Our brain is smarter than we notice...