Eyebot

The Eyebot is a hovering robot similar to the pre-War Floating Eye bot, but with whip-like radio antennas resembling long "whiskers" pointing to its back, like in the Sputnik Soviet satellite, and loudspeakers in the front.

Used by the Enclave
Eyebots are used by the Enclave on the East Coast for broadcasting Enclave Radio, which consists of propaganda, presidential speeches, and patriotic marching music for the people of the Capital Wasteland. These propaganda broadcasts, delivered both over in-game radios, the Pip-Boy 3000, or via the robot's loudspeaker, mention that the American Government is watching, and will eventually rise to restore the former glory of the United States. If Raven Rock is destroyed, the robots will broadcast static.

Eyebots are armed with a weak laser, but are neutral to the player and other civilians (i.e. Wastelanders). They will attack enemies like Raiders and Giant Ants. The Brotherhood Outcasts also have a mutual animus with the Eyebots (due to faction dispositions), and presumably the Brotherhood proper do as well (you will never see this, though, as the two do not share a sphere of influence). The Eyebot has little health and explodes when destroyed, causing damage to anything close, including the player. Combined with their low experience reward and no loot (except in rare cases, and even then it's only one piece of Scrap Metal), making the effort to destroy an Eyebot is entirely wasteful. It appears that even though common sense might lead one to believe they are allied with the robotic enemies, rogue Protectrons and Robobrains have been observed destroying them. Despite being initially friendly, Eyebots will attack anyone (including the player) they see fighting against Enclave forces.

Crow will give you a helmet made out of an Eyebot called Crow's Eyebot Helmet if you invest in him. Another Eyebot Helmet can be found during the final portion of The Waters of Life quest.

Random explosions frequently heard in the distance while roaming the wasteland can mostly be attributed to an Eyebot self-destructing from damage.

Combat Statistics
Eyebots are hardly strong opponents, and the fact that they are (initially) friendly and will attack enemies that engage the player or other Wastelanders means that they are more beneficial than anything else. However, once the player finishes The Waters of Life (or provokes them), they can pose a threat, especially in the former case where they will turn hostile if Enclave patrols are under attack.

The Eyebot packs a small laser weapon, roughly equal in strength to an AEP7 Laser Pistol. It is frighteningly accurate with this weapon, and will rarely miss, even over considerable distances. While not a very damaging opponent, the Eyebot's mobility, small size and high accuracy can make it a threat, especially if encountered in packs (as some Enclave Field Bases make use of them). Fortunately, they are not very durable and easily destroyed, even with fists; they're the most fragile robot in the game.

A note for those trying to destroy an Eyebot early on (such as the one right near the town near Vault 101) - Eyebots explode when killed, causing damage to anything close by. Though high-level characters have little to fear, this explosion can be very dangerous for characters just starting off. Because Eyebots are worth a paltry amount of experience anyway, it's generally a better idea to ignore the little things entirely unless they're hostile. Also, as Eyebots attack most hostile creatures they can often be used as a distraction for creatures such as Deathclaws and Albino Radscorpions (sometimes Eyebots will be floating too high for Radscorpions to reach) allowing you to either attack them or escape.

Because Eyebots explode, they rarely leave a corpse. They will leave a corpse if killed with a critical hit, however. One way to accomplish this is to un-equip your weapons and punch the Eyebot until its health is near zero, then enter VATS and deal a few blows to it. Laser and plasma weapons will leave an ash or goo pile, respectively, if a critical hit is scored. The corpse will contain one piece of Scrap Metal.

It has also been found that Enclave Eyebots will put a mind control device on a Deathclaw and control it. (confirmation?)

Appearances
This robot appears only in Fallout 3, but is similar to the Floating Eye Bot from Fallout and Fallout 2.