Theories that Relate Gravity, Electricity, and Magnetism There are some people who (without having a stated theory that I know of) insist that Gravity, Electricity, and Magnetism are related. Some point to symmetry in Maxwell's Equations as a potential indication of this (intuitive) connection. Is it possible that there are "Maxwell-like" equations that relate Electricity and Magnetism directly to Gravity? All forms of electromagnetic energy do interact with gravity. Are there any physicists who are working on this sort of theory?
 A: For example, Kaluza Klein theory considers a 5-dimensional spacetime where the $g_{5\nu}$ and vice versa terms of the metric produce your electromagnetic potential ($g_{55}$ is introduced as a new term, the radion/dilaton field). This is of course a unified theory of gravity and electromagnetism -- its ideas are also extended to cover more forces in supergravity.
There are other ways to interpret the word "relate" -- for example, "analogies between". A formalism that produces analogies between general relativity and electromagnetism is gravitoelectromagnetism.
A: I know two (non-mainstream) distinct ways.
Because this simple Question atracted downvotes I will have to say something in defense: 
A particular physics viewpoint that 'is not mainstream' do not cast in itself a ban, at least it should not be so. To a physicist minded person there are no taboos. To be mainstream means that, in the present, the main focus of the mindforce is concentrated in the exploration of certain labyrinths that once were hidden behind a closed door. Other doors were closed without further exploration and a  sign was placed at the entrance: Dead End. Some solitary minds pursue the difficult job of digging other labyrints. If they succeed they will be our heros. The only quality that is required is honesty, IMO, as is posted at the entrance of this site.  
Polarizable-Vacuum approach:
Polarizable-Vacuum (PV) representation of general relativity  by Puthoff, 1999  

Having shown by specific calculation
  that the PV approach to the three
  classical tests of GR reproduces the
  traditional GR results  

from the Discussion section:    

alternatively, one can define space as
  Euclidean and time as the same
  everywhere, and discover (from exactly
  the same measurements) how the
  velocity of light, and natural clocks,
  rods, and particle inertias 'really'
  behave in the neighborhood of large
  masses. There is just as much (or as
  little) content for the word 'really'
  in the one approach as in the other;
  provided that each is self-consistent,
  the ultimate appeal is only to
  convenience and fruitfulness, and even
  'convenience' may be largely a matter
  of  personal taste..."

Linked with this paper Polarizable vacuum analysis of electric and magnetic fields by Xing-Hao Ye, 2009    

The electric and magnetic ﬁelds are
  investigated on the basis of quantum
  vacuum. The analysis of the
  electromagnetic energy and force
  indicates that an electric ﬁeld is a
  polarized distribution of the vacuum
  virtual dipoles, and that a magnetic
  ﬁeld in vacuum is a rearrangement of
  the vacuum polarization. It means that
  an electromagnetic wave is a
  successional changing of the vacuum
  polarization in space. Also, it is
  found that the average half length of
  the virtual dipoles around an
  elementary charge is $a = 2.8 ×
> 10^{−15}m$

The other approach that I'm aware is explored in Douglas Pinnow book 'Our Resonant Universe'  it follows after the steps of Kaluza-Klein, Goedecke and Haus (and Maxwell ;-) and ...
It is a monography of a model of particles, based only on Electromagnetism (EM), that has only one parameter (electron mass) and derives the particle properties to within 1% of their values (barion masses bellow 0.1%) and does not suffer of the barionic spin crisis.
The model uses only three building blocks: Electron, Pion and Muon.
The concepts of Mass, Charge and Gravitational Force became crystal clear, IMO.  
You can have a glimpse of the model and explore further starting from here.
I'm used to see two arguments against the possibility of unification of EM and gravity:
The different scale of the forces and the fact that gravity is only attractive.
IMO both of them can be easily dismissed.  
