Hi rsx -
Yes, you can save fuel by running without an alternator. But you'll use up batteries to do so (you'll ruin your starting battery quickly if you regularly run it down). If it's a financial consideration, you have to do the math to see if it's worth doing.
See
AndrewJ's build thread - he's doing it.
I've also done lots of alternator-less driving in the summer months (though none yet this year).
Solar panels are prohibitively expensive, and you'd have difficulty mounting enough of them to support your battery - without ruining your car's aerodynamics.