This is something that I have heard/read so many different contradictory claims about over the years.
In high school I was taught that sperm cells have a lot of mitochondria because they need a lot of energy quickly. This made sense to my adolescent mind.
When I was an undergrad, my one microbiology lecturer swore up, down and sideways that they did not have mitochondria. She never gave any reason or evidence, but I had gotten used to the idea that high school info was often out of date and, sometimes, completely incorrect, so I let it slide.
Then I was reading an article for a paper several years back and it said that, not only did sperm cells have mitochondria, but they did not lose them all. That in fact, some were preserved and engaged in genetic recombination with the mitochondria belonging to the ovum (the maternal ones). This contradicts another rule that so many treat as certain, which is that while nuclear DNA is 50% from each parent, mitochondrial DNA is exclusively maternal.
To sum up: Do spermatozoa contain mitochondria or not? And if so, is the recombination I described above likely?