When you are an indoor gardener the same rules apply to your plants as they do to any other type of gardener. Your plants will need water, food, and plenty of light as does the ones grown outside or in a green house. Of course there are special considerations such as temperature and humidity control but they can be overcome with relatively minor adjustments. With that being said, there are some plants that are best left to the outdoor gardener.
The type of plant that won't do well indoors is really dependant on the climate you live in. If you live in a warm area and have the air conditioning or fans on during the day a plant that is used to higher temperature will not do well inside your home and should be left outside. The same goes for the opposite, if your house is overheated a plant will most likely dry out from lack of moisture in the air.
Other plants that are best left outdoors are perennials and bulb plants that need the seasonal rains and temperatures outside to grow again. You could bring some tulips or daffodils inside in a pot but they will do much better outside.
Most trees are best left outside too; by trying to grow certain trees inside you will only have a smaller less sturdy version than its outside mates. If you do decide to grow a tree indoors plan ahead for a transplant that may have to occur. You do not want to wait until the tree becomes too heavy to move. When a larger plant is repotted or planted elsewhere it will usually go into shock - meaning it will not grow for at least one season (it may be more depending on the size and age of the plant).