Light, Fast, and Inexpensive, Recons make excellent scout and harassment units.
The primary role of the Recon is to provide vision in Fog of War games. With 5 vision, Recons have the highest vision in the game, tied with Subs, Missiles and foot soldiers on Mountains, while also being much more mobile than the others. Recons are critical for identifying possible targets in Fog, as units cannot attack what they cannot see.
Even if Fog of War is not enabled, recons still have situational uses. Being inexpensive and very fast, Recons are excellent at disrupting enemy Capture operations in the early game. Note that because of their Movement Type, Recons need long stretches of Roads, Shoals or Properties to travel over to reach the front line quickly, as they are slowed by Plains and slowed even more by Forests. If there are few routes of transportation that allow it to travel quickly, it may be wise to forgo using Recons for harassment. If the Recon fails to disrupt any captures, you will be put at a disadvantage. Sturm's Recons are notorious for their rushing capability, thanks to their ability to traverse Plains and Forests without being slowed.
In combat, Recons are mediocre attackers at best. They can only deal high damage to foot soldiers, and deal middling damage to Indirect Units. Any other Direct Combat unit (save for other Recons) will handily beat the Recon in combat, unless they are severely weakened. As such, recons are rarely seen outside of the early game or Fog of War matches.
If your opponent builds an early Recon to try and harass you, the best course of action is to build a Tank to counter it as soon as possible, while not hurting your own production capabilities in the process. Use the Tank to support capturing Infantry and deter the recon. Should the Recon attack an Infantry within the Tank's range, attacking it with the Tank will severely cripple the recon, effectively neutralizing it while your Infantry's capture may be slowed by a turn.
Outside of the early game, the only threat Recons pose is to any Indirect units you may have, as they can quickly navigate through any holes in your defense to attack a vulnerable unit. While they still do moderately high damage to foot soldiers, they are unable to completely destroy Infantry in one attack, even with multiple attack boosts. Overall, recons are a low-priority target when faced with other threats, and as long as your Indirect Units are protected, will be unable to accomplish much on their own. Recons take high amounts of damage from just about any unit that can attack it, with the exception of Infantry.
In Fog Of War, Recons may be a valuable target to attack. Even if your units are not fully defended, an enemy cannot engage any units that it cannot already see beforehand, so neutralizing any Recons may limit your opponent's attack options with severely reduced vision. Just be sure to completely destroy the Recon if you plan to do this, as a 1 HP Recon can see just as far as a 10 HP one.