We rent an apartment too, but short of some physical home improvements I haven't found this to be any more difficult for our green living than having a house (we owned our last place). There are even plenty of temporary improvements you can make to the apartment. In fact, being part of a larger building may even keep us a bit insulated, and helps keep our carbon footprint down.
Some things we did when we moved in:
-Turned down the water heater. It was set to 160° so we turned it down to 120°
-Replaced the shower head with a low-flow shower head we had from before (we kept the one that came with the apartment and will put it back before we move)
-Replaced all ceiling fixture lights with CFLs (again, we kept all the bulbs that were here and will put them back when we move out)
-Turned up the temperature on the fridge so that it's just cold enough for our food
-There's no recycling here in the complex meaning we have to drive all recyclables to the solid waste center, so we bought 4 stackable bins that sit at the front door for sorting recyclables, then I take them all out on my way to the grocery store
Since we're stuck with whatever heating/cooling options we have and we live in the south, we:
-Wear as little clothing as possible before turning to the A/C
-Run the A/C at the warmest comfortable setting
-Keep blinds closed during the day
-Open windows at night if it's cooler then (these days it's usually not) and close before the sun comes around in the morning
-Turn on ceiling fans before turning to A/C, and use ceiling fans to help supplement A/C when we really do need to turn it on
Also, we:
-Dry laundry on a drying rack in the office (second bedroom) to avoid using the dryer (this also helps keep it cooler in here!)
-Turn on the lowest amount of light possible (e.g., I don't need the 4-bulb ceiling light when sitting at my computer, so I turn on my 1-bulb desk lamp)
Our electricity is at a flat rate so it doesn't matter when we run stuff, but call your electric company and see if they have different costs for peak times and off-hours times so then you can run your washer, dishwasher, anything that needs to be charged or otherwise running, maybe even shower during off-hours.
That's all of the apartment-related stuff I can think of for now!