High Speed USB 2.0 (as a note, you can actually make a low speed "USB 2.0" device) is rated at 480Mbps and typically attains on the order of 250-300Mbps. This is more than enough to stream a Blu-Ray at native speed (54Mbps max by the spec). The drive probably can't read the disc much faster than maybe 150Mbps (a 2x drive is rated 76Mbps), so plenty of room to spare even for full speed ripping.
Hard drives can go faster. A low end 5400RPM consumer grade 1TB SATA drive can usually hit at least 500Mbps, which is a fair bit about the typical real-world performance of High Speed USB 2.0, but it's not crazy limiting. A mid-range 7200RPM drive (not commonly found in off the shelf externals, but you could build one up yourself of course) can usually hit 750-1000Mbps or even faster, so High Speed USB 2.0 would be fairly limiting (easily restricting it to half its potential speed). High end USB flash drives are frequently capable of 1000Mbps or more, now, so superspeed USB 3.0 really shines, there.
The 12Mbps (real world typically 8-10Mbps) offered by Full Speed USB (1.1 or 2.0, and yes, "Full Speed" is slower than "High Speed") is quite limiting for many forms of video streaming. You can just barely fit a typical DVD into that, and any form of uncompressed or modestly compressed (e.g. MJPEG as used by many webcams, DV, HDV, etc.) is simply way too fast. High Speed USB 2.0 is more than enough for all but uncompressed HD, though (uncompressed 480p at 29.97fps, 16bpp 4:2:2 is ~180Mbps). Note that this means you could run a 720x480 dumb framebuffer at usable framerates on High Speed USB 2.0. High Speed USB 2.0 can also keep up with DV, HDV, etc. from a consumer camcorder.
Super Speed USB 3.0 is nice for external video because you can run realistic PC resolutions without needing lossy compression or relying on lossless compression that's content dependent (and therefore may affect your framerate depending on what you need to redraw), but it's not really necessary for any form of compressed video. I guess you could also use it as a replacement for HD-SDI or DVI/HDMI/DisplayPort when capturing from a prosumer/professional video camera, but I'm not aware of any actual implementations at this time (USB Video Class should support it, though).
As for backing up "large" amounts of data, things take a while. At 1Gbps transfer rate (e.g. 1Gb Ethernet which gets surprisingly close if your PCs can keep up), you need about 3-4 hours per terrabyte at real-world speeds. Note that your hard drive is not much faster unless it's an SSD or RAID array (0, 5, 6), so you won't see much benefit of Super Speed USB 3.0 (5Gbps, real world varies highly due to a ton of factors) compared to gigabit Ethernet, but Super Speed USB is of course also a viable option. Super Speed USB mass storage should be comparable in speed, assuming your CPU is free, to a direct SATA connection (to include eSATA).
SATA can attain close to 6Gbps in the real world (which, note, due to the 8b/10b encoding means 600MB/sec, not the "obvious" 750MB/sec), but even a high end SSD will have trouble keeping up with.
If you've got a high end SSD on both ends of the copy connected directly to the PC via SATA, you should be able to copy 1TB in a bit over half an hour. Super Speed USB 3.0 should, with good hardware, run a bit more than half that speed, so 1TB would take about an hour, and you no longer need a "high end" SSD to keep up. Doing the same 1TB copy with High Speed USB 2.0 as the bottleneck would take nearly 8 hours, but you no longer need an SSD (just a middle of the pack revolving metal drive) to keep up.
If you want to copy 2TB, just double all those transfer times, of course.
FWIW, if Gigabit Ethernet isn't fast enough for you, 10 Gigabit Ethernet does exist and is rapidly becoming remotely affordable for consumer usage. For the time being, there's no way any single other interface on your PC can keep up unless you have Thunderbolt (well, or you consider 4xPCIe, but you can't really hook that directly up to anything useful). There's also a 40Gb and 100Gb Ethernet standard, but you (probably) can't afford it, and nothing you own (probably) can really keep up, anyway.
TL;DR: High Speed USB 2.0 has started to become limiting for external mechanical hard drives, though not by huge factors. For high end external flash media (SSD, some "thumb drives", etc.), it can be very limiting and the higher speed offered by Super Speed USB 3.0 can make a major difference. It's also nice for uncompressed HD video, but it isn't even remotely needed for compressed sources used for streaming and consumer media.