Q:

Can any dynamo hub get the electricity rotating with the spokes?

I want to make wheel LEDs powered by a dynamo hub. I was wondering if that's even possible. Any ideas or models?

A:

Reelight do something similar but opposite: they mount magnets on the spokes and the light and coils on the frame.  This demonstrates that it's broadly possible.  You'd need to mount the magnet on the fork or seat-/chain-stay with a coil and light on the wheel.  This gapped dynamo arrangement won't be very efficient, but wheel lights don't need to be as powerful as headlights.  This is the most promising approach, and could be tested with basic kit (I'm tempted to play myself, but have work to do).  For experimenting, I strongly suggest working on the back wheel - if something breaks and jams the wheel, you're much less likely to get hurt than if you jam the front wheel; testing on a trainer would also be possible if you have access to the right type.  Yes it's harder to see what's going on, but a camera/buddy would be better for that anyway.  Also you can spin the back wheel fast more easily for a bench test, by hand-cranking the pedals.
An alternative approach would require electrically insulating spokes. Carbon fibre spokes exist but are expensive and rare.  You may be able to get an insulating washer under the nipple, perhaps using an anodised nipple as well.  You'd then set up one connection through the hub and the other using a brush (or single copper spring) against the rim (beware wear on your rim, use one that's brake-compatible).  Neither connection would be great.
One thing that wouldn't work is adapting one of those torches (flashlights) that works by shaking a magnet in a coil (notionally strapping it to the spokes).  At speeds over about 6 km/h (4 mph, walking pace) the centrifugal force will push the magnet outwards more the gravity will pull it downwards (you can tweak things to roughly double this number at best.
Something that could be made to work but would  be dangerous is mounting a bottle dynamo inside the spokes, with a ring-shaped track attached to the frame for it to run on.  I mention this only to dismiss it, and don't recommend it

A:

This is more an electricity problem, incidentally related to bikes, so this is not really a good place for it, however, I'd give it a try.
Normally a dinamo is designed to use the electricity in the non-rotating part. To use the electricity inside the rotating wheel yo would need the opposite design. As for it being an unusual situation, it's not probable that a commercially available solution covers that need.
In the DIY realm, you would need to use brushes (like the ones in DC motors) but those are designed for tight tolerances and small distance, and have the wear problemas associated with them.
At least theoretically, you could implement a brushless design in reverse. A brushless motor uses magnets in the rotor and coils in the stator. The coils are energized switched from one polarity to another by an electronic controller. These motors can work as a generator: if you spin the rotor, you move the magnets relative to the coils, inducing voltages in them. You can either use the alternate current coming from the coils or connect diodes to rectify and obtain DC (or pulsing DC).
If you want to consume the electricity in the wheel, that is, in the rotor, you need to swap the design and put the magnets in the fixed part (the frame) and the coils in the rotating part (the wheel), probably in the spokes. As the coils move past the magnets, they should create a small voltage. As both the coils and the LEDs would be in the wheel, you would't need spinning or sliding connections. The magnets can be arranged on a small arc shaped piece, placed on the seat stays, near where the rim brakes would be mounted. The magnets should be placed alternating polarity and there should be a few pairs. Then a few coils are placed on the spokes. The arch should be such that the coils pass near all the magnets when rotating the wheel.
If you wire each coil individually to a L.E.D. it should light up as its corresponding coil passes near the magnets, so they will illuminate near the stays only. If you interconnect the many coils correctly, you can achieve all round lighting.
An advantage of such design is that once set up, it would light every time the bike is moving and would not need any switches.
A few trial and error hours should be enough to determine how many turns the coils need. L.E.D. do not need a lot of current and voltages ranging between 1.2 - 5 volts. For more in depth information regarding wiring, amps, etc, You should definitely consult an electronics related site.
Remember that a bike wheel normally flexes quite a bit when in normal use, that should be accounted for in any design.
Anecdote
When I was a teenager (around 1998), I taped a 9 volt battery to the hub, right in the middle of the spokes, and wired it to a few Christmas light bulbs placed on the spokes, near the rim. I used a centrifugal switch out from a yo-yo (A small weight placed on the end of a thin flexible metal strip.) I just affixed it near the rim. The wheel structure (common steel hub, spokes and single wall rim.) was one conductor and the other was a cable running in series for each bulb and the switch.
It worked kind of fine. When the bike reached some speed, the lights would turn on and turn of when I was going too slow. It was difficult to tune the turn-on speed and the mounting of the switch was flimsy so hitting a pothole threw it off.
If I where set to do this again, I'd use a small portable power bank for rechargeability, strapped to the hub (being close to the center of the wheel diminishes the rotational inertia problems. Zip ties are light and sturdy enough to affix the L.E.D.s. For switching I'd either place a manual switch near the hub or attempt a better built centrifugal one. Another option would be a transistor used as a relay activated by a reed switch or a vibration activated switch. 
Practical alternatives to this
These only achieve the visual effect, but are not rechargeable, auto switching and not non-discardable.
I've seen lighted valve caps. Some of then may have integrated centrifugal or vibration sensing switches. I guess you can glue some of those or zip-tie them to the spokes if you want more than one spot around the wheel. I do not think they are rechargeable or even have a replaceable battery.
There are small bike lights that come in an elastic rubber casing intended to be strapped to the handlebar or any tube of the bike. Those can be easily strapped between two spokes and/or zip tied. They run on coin cell battery so are not rechargeable and would need to be individually and manually switched on and off.

