Does combustion have to produce gaseous CO2?

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You could think of oxidizing alkanes only partially, e.g. to formic acid. However, formic acid is toxic and also volatile. So in praxis not much easier to store than liquid CO2.
An exotic possibility would be the reaction 5C+3/2 O2 +CaCO3 -> Ca C6O6, the latter being known as calcium rhodizonate. A solid, very appreciated in analytic and forensic chemistry. Would be interesting to know the enthalpy of the reaction.
 
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Simply put CO2 and H2O are the thermodynamically stable products obtained when burning hydrocarbons. Of course multiple intermediates exist but these are all radicals and highly reactive. In order to burn hydrocarbons in a controlled fashion, think of biochemical processes. These require highly complex supramolecular machineries to convert sugars into CO2 and H2O aerobically and lactic acid or ethanol anaerobically making use of relatively stable intermediates. I'm not even sure if it would be possible to halt these reactions in the presence of O2 to get something like an ethanol product. Probably more radical chain reactions would be induced. So producing anything else from hydrocarbons in the presence of oxygen than CO2 and H2O is unlikely.
 
I think certain metals can be "burned" (perhaps oxidized in a solution, or whatever). Aluminium comes to mind.

Of course we need to make the aluminium first, which takes energy. Energy from other sources (nuclear power, solar) could be concentrated for use as fuel in aircraft or the like, or CO2 could be made into octane (gasoline) which would be carbon neutral when it was subsequently burned.

These technologies are all relatively expensive currently.