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Ivy is a tough little bugger. They're somewhat invasive species, popping up in places where they haven't been planted. It can be damaging to structures and can smother trees (like the ivy in the front is trying to do to one of our trees). I don't like the stuff when it's not in a container. That being said, it is easy to root, can be variegated or have different leaf forms. I think English Ivy is the most popular species, with many varieties. It works well in pots.

Cacti and succulents can be good, but people tend to think they don't need any water at all or don't water them frequently enough. Many of them prefer full sun, but can live with less light than that. I seem to be doing very well with Christmas cacti, having rooted several and I even have one blooming heart . Hen and Chicks is a popular group(I think in Cunningham, they are "house leeks")(also live-for-evers, though I know you can kill them sweatdrop ), as they are not spiky and form pretty rosettes of leaves. My dad rarely waters them, so if I'm not around... they die. They're easy to propagate, as just a single leaf will root. Getting them to some size afterwards is the hard part. All of my cacti are from pieces that had fallen off of adult plants.
Aloe was also mentioned. I think ours are suffering from not getting quite as much light and water as they would like. They're all kinda small.
There are various tropical vines and plants. My Grandmother has Hoya(wax plant), which has star shaped flowers that have five points. It is doing well despite being in a window that is northwards. I haven't seen it in stores, but I'm sure with the internet you can find it. It is a rootable plant as well. I can't think of too many tropical plants off my head, but there are numerous species. I would go for one that takes partial sun to full shade, as those light requirements are easier to meet. Many of them are moderate water wise, so they'll probably need to be watered once a week in a well draining pot. You want to make sure your pot drains adequately lest the roots rot.
Hmmm there is a plant called an airplane plant. It sends off little baby plants on these stems that hang off the plant (if you have it in a hanging pot). It seems pretty hardy and can do with lesser amounts of light. It's also easy to propagate. There are those potted figs that do well as indoor plants too, as long as you remember to water them.

Unless you have a south facing window that gets sun, many times full sun plants won't get quite enough sunlight (you'd be surprised how much light is actually filtered out by some windows). I tried to keep a sundew, but it died because there wasn't enough light gonk . Some plants should be supplemented with a grow lamp, which I would suggest if you want it somewhere not right next to a window. You could put it on a timer so that it can have regular periods of light (I have my fish tank’s light on one). Buy a timer from the lighting section, not in the plant or pet area. They over price it if it is "for aquariums".

I have a lot of mums in my backyard but my chrysanthymums are the ones that grow like crazy. They are growing up the window in my living room.

When a plant grows for too long in its container, it generally becomes root-bound. With no room for additional growth, roots become tangled, matted, and grow in circles.
Root-bound plants placed in the ground without having their roots untangled often fail to overcome their choked condition. This results in stunting the plants growth and potential

Red or pink or I may have one of each.