Some of the number of times Captain Kathryn Janeway has broken the Prime Directive:
Caretaker
In this, let us remember that the Prime Directive states that interference with the natural development of any race which possesses a lower level of technology than the Federation is strictly forbidden. Had Captain Janeway not interfered, the Kazon would have taken possession of the Array, this being the natural course of events for their race given the circumstances. Captain Janeway's destruction of the Array was therefore a clear violation of the Prime Directive. Captain Janeway's claim that by destroying she was protecting the Ocampa is mere fabrication, as we have seen.
Jetrel
Captain Janeway allowed a known war criminal of a race with a lower level of technology than that of Voyager use of the Sickbay and the transporter. Her logs indicate that she sympathized with him, as he was trying to undo damage he had done, but the fact remains that she aided and abetted a criminal and violated the Prime Directive.
Prototype
The Voyager crew beamed aboard a deactivated robot and Janeway allowed Torres to try to reactivate it, using Federation technology. Once revived, the robot insisted that Torres build a prototype power module for the construction of additional units. Belatedly Janeway insisted that this was a violation of the Prime Directive, but the robot kidnapped Torres. Once aboard their ship Torres created the power units they needed, only to destroy them when she found out their true plans. The fact that the technology was destroyed does not excuse the original Prime Directive Violation.
Basics
By surrendering Voyager to the Kazon rather than destroying her, Janeway not only violated the Prime Directive by placing all of Voyager's technology in the hands of the Kazon, but conducted herself in a way unbefitting an officer, showed her unfitness for command and aided and abetted the enemy.
Swarm
Captain Janeway willfully invaded an alien realm of space and proceeded to destroys hundreds, if not thousand of their vessels - thus changing the balance of power in that section of space, ignoring the rules and culture of a sentient alien race and breaking the Prime Directive.
Scorpion
Captain Janeway made a deal with the Borg, confirmed enemies of the Federation, to help them destroy an enemy of their own in exchange for free passage through their space. Her reason for striking this deal is quite clear: passage through this particular area of the Delta Quadrant was the shortest route to the Alpha Quadrant. Going around Borg space would add decades to their journey. Although the deal Captain Janeway struck with the Borg did gain them the passage they needed, the Borg subsequently turned on them, becoming once again the enemy of Voyager. In addition, Janeway made a powerful enemy of the species she helped the Borg to defeat: a species the Borg designate 8472. This incident once again brings into question Captain Janeway's fitness for command as well as her original decision to strand her ship and crew in the Delta Quadrant, not to mention she broke the Prime Directive once again by interfering in the cultures and problems of Species8472 and The Borg - her decision to help the Borg led to millions more races being assimilated(as seen in 'Hope and Fear') and several thousand alien cultures ceasing to exist.
Demon
Captain Janeway allowed a pre-sentient lifeform to sample the Voyager crew's DNA. The pre-sentient "silver blood" lifeforms became humanoid as a result, and quickly mimicked the crew's mannerisms, memories, and technology. The Prime Directive is designed to prevent interference with the development of lifeforms less advanced than those of the Federation. Most often, alleged violations of the Directive arise from technology transfer or the exposure of pre-warp civilizations to the existence of alien life. The violation here, in many ways, is much more severe, as the evolution of an entire species, not merely the development of a civilization, was irrevocably altered by Janeway's callous actions. Indeed, there is anecdotal evidence, not corroborated in Voyager's logs, indicating that these lifeforms came to believe that they were in fact Voyager's crew, and they all died in a futile attempted to return to Earth. If true, this underscores the importance of the Prime Directive and the terrible consequences that can result when it is violated.
The Killing Game
On several occasions, Captain Janeway improperly gave Starfleet technology or technological assistance to Delta Quadrant races. In the best-documented incident from this time, on or around Stardate 51710, Captain Janeway gave Federation holodeck technology to a race called the Hirogen. Three years later, it was discovered that Hirogen abuse of that technology resulted in the creation of a sentient and violent breed of hologram. Those holograms subsequently killed several sentients. In a documented conversation taking place on or around Stardate 54300, it was revealed that trading technology for supplies had in fact been standard operating procedure aboard Voyager for some time. Not every incident is fully documented in the ship's log, but a pattern of improper trade and its often dire consequences is easily seen in the record.
Dragon's Teeth
Captain Janeway ordered her crew to revive a race called the Vaadwaur, who were found in suspended animation on a devastated planet. The Vaadwaur had in fact been a violent, predatory race that had been defeated and nearly wiped out by its victims centuries earlier. As a result of Janeway's actions, several Vaadwaur vessels escaped to threaten that area of space once again. Sworn testimony from Ambassador Neelix and Crewman Annika Hansen will demonstrate that Janeway did not wait for a historical records search to be completed before having the Vaadwaur revived. That search revealed the true nature of the Vaadwaur, but by then it was too late to prevent their reintroduction into the Delta Quadrant.
Riddles
Captain Janeway negotiated with members of a paranoid and xenophobic race called the Kesat, offering them tactical data on neighboring races in exchange for information needed to treat Commander Tuvok, according to sworn testimony by several members of Voyager's bridge crew. While Voyager's log indicates that a deal was not in fact struck, Janeway's willingness to make such an arrangement demonstrates a disregard for sentient life and for Starfleet's principle of non-interference. A Starfleet Captain has a duty to protect the members of his or her crew but not at the expense of innocent sentients.
The Voyager Conspiracy
Captain Janeway ordered her crew to assist an alien named Tash in building a "subspace catapult," which was subsequently used by Voyager to travel several thousand light years closer to home. The crew used Starfleet technology and methods to build the catapult, but Janeway did nothing to prevent the catapult and its component Starfleet technology from falling into the wrong hands after leaving it behind.
Live Fast and Prosper
Captain Janeway discovered that the complete contents of the Federation database had been stolen from the Delta Flyer. While Voyager's crew apprehended the thieves, who were impersonating Federation representatives, Voyager's log shows that Janeway made no effort to determine whether that data had been passed to others, creating the possibility that the Delta Quadrant could now be awash in Federation knowledge and technology.