Usually when I see lists of things to do to be more energy efficient, they require one to own their own home. What can I do to be more energy efficient in an apartment? 
For example, I can't install solar panels, I can't upgrade/change my appliances, I can't install better insulation or windows, and I can't install a programmable thermostat. 
Pretty much the only thing I can do (and have done) is switch all of my bulbs to CFLs. I also keep all of my electronics on power strips which I turn off when I leave my apartment and when I'm sleeping.
What can I do that would make a significant difference that doesn't require any renovations or installations?

There are several things you can do to be more energy efficient in an apartment that don't require any major renovations or installations. Here are some ideas:

1. Seal air leaks: Use weatherstripping or draft stoppers to seal air leaks around doors and windows. You can also use foam sealant to fill gaps around electrical out
What are some other things I can do that don't require any major changes to the apartment or purchasing expensive items? 
I'm not terribly concerned about the cost, just looking for ways to be as energy efficient as possible. 
Thanks for the help!
There are several energy-saving measures you can take in an apartment that don't require major renovations or investments in new appliances or fixtures:
1. Use energy-efficient lighting: