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
I also turn off lights when I leave a room and if I've forgotten and left them on for a short time, I use a timer. 
Are there any other little things I can do to be more energy efficient? 

Absolutely! While you may not have the ability to make major home improvements, there are still several steps you can take to conserve energy in your apartment. Here are some suggestions:

1. Use Energy Star Appliances: While you