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, in preparation 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. The Eyebot has little health and explodes when destroyed, causing damage to anything close including the player (making it even more pointless to attack them since there's no loot, and you waste bullets unless you melee them, in which case you get hurt). It appears that even though common sense might lead one to believe they are allied with the robotic enemies in the waste, 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 Waters of Life escape.

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, but Eyebots can still pose a threat, especially after the Waters of Life quest in which they'll move to protect Enclave patrols and guard stations.

The Eyebot packs a small laser weapon, roughly equal in strength to an AEP7 Laser Pistol. It is frighteningly accurate with this weapon, and rarely seems to 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 one's 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.

It seems Eyebots do leave a corpse, but it must be killed in a specific manner. Un-equip your weapons and punch the Eyebot until its health is near zero, then enter VATS and deal a few blows to it, and sometimes the Eyebot will leave a corpse. Also, if killed by a deathclaw or Yao Guai, they may sometimes leave a corpse. They sometimes contain Scrap Metal, but it seems the possibility for the item to spawn on the ragdoll is 25-50%. If you use a flamer or heavy incinerator, the eye bot will, possibly, not be destroyed. A critical hit with a plasma weapon will result in the Eyebot leaving behind a Goo Pile corpse, which can be similarly looted for a piece of Scrap Metal.

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