To answer the headline question straight-away: No, it's almost impossible to find a 1080p / 60FPS webcam for use with Twitch.tv streaming or YouTube. The issue is a matter of bandwidth; it'd require more bandwidth than is reasonably possible through most modern interfaces, and so the hardware doesn't exist at any affordable price. You'd have to buy an actual prosumer digital video camera, then hook that up to the PC – and there's a decent chance you'll still be limited to 720p60, depending on the camera.
But it is possible to get high-quality webcams at 1080p, 30FPS – which is plenty for almost all streams. If you're vlogging regularly, no game streaming in the background, it may be worth looking into an actual video camera for the absolute highest quality. For game streaming, a 30FPS output is fine, as the video output will normally be shrunken and shoved into a corner of the stream (with the game taking up the majority of the screen).
Let's run through a few of the top cameras.
Its MSRP is $99.99, but the Logitech C920 can regularly be found for around $60. This is an end-all webcam for most streamers. It's capable of 1080p (16:9 widescreen) streaming, and easily mounts to a tripod or to the top of a monitor. We'd recommend a small, cheap tripod if you'd prefer a different angle than top-of-monitor affords. A six-foot cable makes it easier to run the camera from a tripod.
The camera connects via USB and supports Mac OS, Windows, and Android. Software is available, but not necessary – just use XSplit or OBS to do most of your setup.
Low-light correction is built into the C920, but will slow down the framerate for poorly lit scenarios. See the bottom of this post for a solution to that.
The C920 cannot perform at 60FPS, but will push 1080p30 or 720p video. Face tracking and motion detection are available, but not necessary to be used.
Unfortunately, the C920 can't pivot side-to-side, only up and down. This might be an issue for some setups.
The Microsoft H5D LifeCam Cinema is slightly cheaper, and can usually be found at around $53, but drops down to 720p. The biggest advantage of Microsoft's LifeCam Cinema (other than the slightly reduced price) is that it's able to pivot left and right. The LifeCam Cinema is a widescreen camera that shoots 720p at 30FPS, has low-light correction (but should still be accompanied with a light), and can auto-focus as the scene changes (the C920 can also do this).
If you desperately need something that swivels side-to-side, consider this as an alternative to the C920.
Tighter budgets necessitate some cuts to quality, unfortunately – but if it's a cheap camera or no camera, it's worth at least getting something cheap.
The Genius F100 is a 1080p camera with a 30FPS throughput, but will struggle harder in low-light than some of its competition. Still, the camera is usually about $32 and among the most affordable 1080p webcams on the market. The Genius F100 should be focused manually (somewhat of an annoyance, but probably something only done once if most use is sedentary) and used with a good amount of light.
Don't Forget Light
A camera is only as good as its light; in fact, proper light can make almost any camera perform well. A camera also requires a lot more light than the human eye to perform well. You can grab a $30 light and tripod mount it (or lean it on something) to instantly improve the video playback.
If you're having issues with low framerate or FPS drops on your webcam, it's probably because the camera is attempting to compensate for low light by slowing down its shutter speed (and thus the frame rate). Something like the Neewer 160 LED light would work. If that's not cutting it (your room is very dark), consider some studio lights.
Check our streamer advice blog for more support, and for additional guides on gaming and streaming accessories.