There is no evidence whatsoever that the Federation has had any kind of armoured vehicle in its entire history. Its approach to the problem of troop mobility and firepower seems to be the use of airlifts and transporters, both of which present special vulnerabilities.
Airlifts can be attacked from the ground or from the air. A mortally wounded Federation trooper in "Nor the Battle to the Strong" made reference to a "hopper" which was obviously some sort of air lift. He said it was taking a pounding as it tried to lift off, and it was implied that he had sacrificed his own life in order to attack Klingon ground troops and distract them long enough to let the vehicle make its getaway. This was obviously an attempt on the part of the writers to evoke parallels to the Hueys that would extract men from combat zones in Vietnam, and it seems that the Hopper is analogous to the Huey. It's air support, not mobile armour.
Transporters present vulnerabilities of their own. We learned in "When the Bough Breaks" and "Realm of Fear" that they are better at insertion than extraction, hence the common practice of sending men from one ship's transporter pad to another ship's transporter pad, hence tying the two systems together. We learned in "Skin of Evil" and "Tin Man" that telekinetic forcefields can block transporters completely. We learned in "Symbiosis", "Suspicions", and "Quality of Life" that they are erratic, unreliable, and sometimes completely useless in the presence of ionizing electromagnetic radiation. We learned in "Royale" that an environmental containment forcefield can block transporters even when it permits communications to pass through. We learned in "Ensigns of Command" that transporters don't function in entire star clusters where "hyperonic radiation" is present (although no one knows what hyperonic radiation is) and that they can be rendered useless by the mere presence of certain unusual subatomic particles. We learned in "The Enemy" and "Power Play" that transporters don't work through naturally occurring atmospheric electrical storms. We learned in "The Hunted" that a sudden movement can disrupt a transporter beam. We learned in "The High Ground" that transporter locks are more difficult than simple visual acquisition, ie- it's possible for something to be visible to the naked eye but impossible to acquire with a transporter sensor system. We learned in "The Most Toys" that certain substances can't be transported at all. We learned in "Legacy" that the electromagnetic fields generated by an ordinary electrical transformer can prevent transport locks, and that they can't transport through 2 km of solid granite under any circumstances. We learned in "Second Chances" and "Final Mission" that the natural fields emanating from certain inhabitable planets or moons can prevent transporter use completely. We learned in "The Host" that transporters put stress on the transported subject, and that it may therefore be dangerous to transport wounded personnel. We learned in "Darmok" that an energetic ionosphere can block transporters. We learned in "Hero Worship" that they can't transport through "victurium alloy" bulkheads, thus leading to the obvious question of what other materials are opaque to transporters at that thickness. We learned in "Schisms" that transporters don't work in the presence of nucleonic radiation. We learned in "True Q" and "Lessons" that atmospheric ionization can prevent transporter use entirely. We learned in "Descent Part 2" that all of the transporters on the entire USS Enterprise can only transport people at an average rate of 1 person per second. We learned in "Pegasus" that there are dangers associated with transport through large amounts of solid matter. We learned in "The Chase" that tractor beams interfere with transporters, and worse yet, we learned in "Attached" that a cunning enemy can use tractor beams to redirect a transporter beam to an arbitrary spot of their choosing!
Airlifts are no substitute for mobile armour on the ground, but transporters are even worse. In the face of a ruthless and opportunistic enemy (ie- a realistic enemy), a ground army reliant on transporters would find its troops either immobilized by one of the myriad transporter blocking techniques available or worse yet, captured or killed during transport by an enemy who uses distortion fields or tractor beams to disrupt their movement. The Trekkie excuse of "we don't need armour because we have transporters and air support" is oversimplistic and wrong. Both of those things have their legitimate uses, but they don't eliminate the need for armoured fighting vehicles on the ground, any more than Orville Wright obsoleted the automobile when he flew his first plane.
No Federation tank has ever been seen or even mentioned in the entire series runs of Star Trek TOS, TNG, DS9, or Voyager. It is possible that enterprising Federation commanders could buy some sort of armoured vehicle from an independent arms manufacturer in the free market outside their borders (I believe Quark even made reference to one once), but the political obstacles to that sort of activity in the Federation would probably be insurmountable. Worse yet, one must ask the same question that was posed in regard to artillery: even if Federation ground forces can acquire them, how are their troops supposed to use them without any training?
No Federation reconnaissance vehicle has ever been seen or even mentioned in the entire series runs of Star Trek TOS, TNG, DS9, or Voyager. They undoubtedly expect their spacecraft and omniscient sensors to pick up everything, based on the assumption that the enemy will do nothing to obstruct orbital surveillance, aircraft fly-overs, or sensor use.
Mobile Infantry Combat Vehicles
No Federation MICVs have ever been seen or even mentioned in the entire series runs of Star Trek TOS, TNG, DS9, or Voyager.