I'm watching the first two seasons of Voyager and various episodes have commentary on having energy limitations -- but we constantly see crew using extremely complicated holodeck simulations. Why would they allow use of the holodeck if they need to conserve energy?
The holodecks on Voyager run on an independent power source.
This can be seen in the season five episode Night, when main power is suppressed yet the holodeck continues to run. For whatever reason, this power source doesn't appear to require any significant amount of fuel:
SEVEN: Independent subsystems are operational. Environmental controls, holodecks. Reroute power from this holodeck to the emergency relays.
PARIS: Yes, ma'am. No luck. The hologrid is frozen.
In the episode Parallax, there was even a time when Janeway suggests trying to use the holodeck to provide additional power, which Kim shoots down as not possible due to a system incompatibility;
JANEWAY: What about alternative energy sources? Ensign Kim, have you had any luck getting power from the holodeck reactors?
KIM: Not yet. We tried hooking them to the power grid and we ended up blowing out half the relays. The holodeck's energy matrix, it just isn't compatible with the other power systems.
This is in opposition to the holodecks on Enterprise D, which were shut down when the ship was low on power (TNG:Booby Trap).
There actually is a very practical reason for the holodecks to have an independent power source, The EMH. It's true that the Doctor was originally an emergency program, but one would have to assume that if you have an EMH program, it's expected to run primarily when there is a major emergency. Such emergencies require more space than just the infirmary. In DS9 and TNG there are times when the doctors have to house patients in areas outside of the infirmary. If your regular doctor is incapacitated in such a situation, that would mean patients need to be kept where the EMH can go. That means holodecks have to have a power source separate from the rest of the ship. That way, even when power is at a minimum the doctor can treat patients in holographic settings.
There is another factor that we should consider. Though the culture in Star Trek originates from ours, it's not wholly the same. The mental health of the crew is going to be just as important as the physical health of the crew. Hollodecks are not just a place to play silly games, and romp around before sex. The doctor orders Janeway to the hollodecks when she's overworked, they have social events there, and there is a theme program every couple of seasons. I think this shows they are also thought to be a place ensure mental health. And, when you look at how they are usually used, it kind of makes sense. Though people use them for personal use as well, they are most often used for group activities, social gatherings, and it isn't uncommon for a program to run all day with a dozen or more crew members enjoying it at one time.
I suspect that compared to the running of the whole ship, the power needed to run one hollodeck is pretty nominal, and group use of them is a way of being conservative in it's power use, along with solidifying relationships. Given how much they hate Nelix's cooking, allowing liberal use of the holodecks could be the only practical way of improving morale. In many ways, the holodeck programs are like 10 forward.
I think its because the energy that is used to produce a hologram is converted back into the same energy when the program ends. So although a holodeck uses a lot of energy while in use, its just borrowing it, not using it up. They say in Star Trek that transporter and holodeck technology is on the same principal (Energy matter convection. Or E=Mc2). I think that means these technology are about reorganising energy, not using it. Though some kinetic energy must get used in order for a hologram to interact with a human.
Because if the crew doesn't, they would go out of their minds, being stuck thousands of light years away from home.
The replicators run off the EPS (Electro-Plasma System) conduits which get power from a manifold linked to the Power Transfer Conduits that carry warp-plasma from the Warp Core to the drive nacelles. Apparently they had to choose between using power for the Warp Drive or luxuries like the replicators. As other folks have mentioned, the Voyager Holodeck systems apparently run on a separate system (possibly a fusion reactor?) that doesn't easily connect to the EPS conduits. Voyager needs both antimatter and dilithium crystals to run the Warp Core, and the search for both were central to several episodes (searching for Dilithium crystals in S1E4 "The Phage", and searching for a replacement for antimatter particles in S1E5 "The Cloud").