a few of your suggestions can be summarised to "other electromagnetic senses" (being things of other wavelength than visible light), and generally things not in the "sound range" either.
Magnetic sense has been mentioned several times; I am going to look at getting a magnetic ring; never thought of it; and would be keen to try it. (and the non-invasiveness sounds good to me)
Someone mentioned already - internal vs external senses. I would like the ability to sense my own body temperature (possibly at my extremities vs my core, although I don't think it is known whether these details related to productivity - I would also like to know that), a general feel for my heart rate (this is coming along with wearables, but slow).
in order to sense electromagnetic radiation there needs to usually be a controlled source that you detect. So some kind of emission source of a particular wavelength that you can feel changing. (in the same way that we see different colours because light waves bounce off things differently)
I would like to have a sense of "density" of objects, I often find myself tapping on things to "check" but not really being able to describe why I do that. In addition to this a vibration sense - for the low-audio-wave frequencies of .01-50hz (you can hear them but I would like to feel them and take better note of the patterns they produce)
Perhaps a "purity sense" to be able to determine if a thing was a pure substance or one with imperfections (either a metal or a diamond etc) the value of a pure substance is particularly high because you can have control over the interaction it has with its environments.
Electrical sense (similar to a magnetic sense). To sense either the voltage or amperage or Wattage (V*A) of an existing electrical system. To be able to determine the effectiveness of energy generation (i.e. from a solar panel) without other systems.
Radiation sense. Humans just don't feel radiation till its killing us; even then we don't know what it is (sometimes doctors even fail to identify radiation burns). Would be nice to have (even if I also wish it were less common to not be a sense needed)
A measurement sense for dimensions of size; weight; volume. To be able to get more than a subjective feel for a size of an object. Even after measuring things and writing them down; we still have to trust the ability of our measurement protocol. A classic line from woodworking is "Measure twice, cut once" but for me is "measure twice alone and a third time in front of someone else".
A dietary intake sense. To be able to determine the optimum food intake based on an expected future activity ratio. To automatically not have to worry about being overweight or underweight. Similarly an intuitive "need to exercise" sense (where with things like depression you are demotivated to exercise when it seems to often help).
A meme sense. A sense of understanding of when you are trapped in loops. (I have no idea how to do this other than the hard way)
A gas (or liquid) quality sense, to be able to check the composition of substances for their safety (particularly oxygen content, or presence of heavy metals in water)
(wow this is quite a few)
(Edit: Data processing senses would also be good, even a brain-cache to be able to record a few seconds of sensory information and then reprocess it over the next minute)
What new senses would you like to have available to you?
Often when new technology first becomes widely available, the initial limits are in the collective imagination, not in the technology itself (case in point: the internet). New sensory channels have a huge potential because the brain can process senses much faster and more intuitively than most conscious thought processes.
There are a lot of recent "proof of concept" inventions that show that it is possible to create new sensory channels for humans with and without surgery. The most well known and simple example is an implanted magnet, which would alert you to magnetic fields (the trade-off being that you could never have an MRI). Cochlear implants are the most widely used human-created sensory channels (they send electrical signals directly to the nervous system, bypassing the ear entirely), but CIs are designed to emulate a sensory channel most people already have brain space allocated to. VEST is another example. Similar to CIs, VEST (versatile extra-sensory transducer) has 24 information channels, and uses audio compression to encode sound. Unlike CIs, they are not implanted in the skull but instead information is relayed through vibrating motors on the torso. After a few hours of training, deaf volunteers are capable of word recognition using the vibrations alone, and to do so without conscious processing. Much like hearing, the users are unable to describe exactly what components make a spoken word intelligible, they just understand the sensory information intuitively. Another recent invention being tested (with success) is BrainPort glasses, which send electrical signals through the tongue (which is one of the most sensitive organs on the body). Blind people can begin processing visual information with this device within 15 minutes, and it is unique in that it is not implanted. The sensory information feels like pop rocks at first before the brain is able to resolve it into sight. Niel Harbisson (who is colorblind) has custom glasses which use sound tones to relay color information. Belts that vibrate when facing north give people an sense of north. Bottlenose can be built at home and gives a very primitive sense of echolocation. As expected, these all work better if people start young as children.
What are the craziest and coolest new senses you would like to see available using this new technology? I think VEST at least is available from Kickstarter and one of the inventors suggested that it could be that it could be programmed to transmit any kind of data. My initial ideas which I heard about this possibility are just are senses that some unusual people already have or expansions on current senses. I think the real game changers are going to be totally knew senses unrelated to our current sensory processing. Translating data into sensory information gives us access to intuition and processing speed otherwise unavailable.
My initial weak ideas:
Someone working with VEST suggested:
Some resources for more information:
More?