Houseplants in pots are popular windowsill subjects but broaden your horizons.

No greenhouse or conservatory but lots of windows? Then you can grow a range of plants using the windowsills or a shelf under a window. Chose small plants and pots that are and will be in proportion to the width of the windowsill.
Tender plants may suffer in winter behind curtains but with good double glazing I do not bother moving most plants at night.

On the Kitchen Windowsill

Herbs will be many gardeners first choice and curly or flat leaved Parsley are likely to figure most frequently. Basil  can be used as cut and come again and is available in several varieties so I would add this to any list of windowsill plants.
The hot and steamy conditions of many kitchens don’t help all plants but ferns and Orchids usually like these conditions particularly on North or East facing window ledges.
We currently have a white Saintpaulia which enjoys humidity but it will be moved when the flowers go over to be replaced by a Christmas cactus in flower.
Aloe has grown on a shelf near our window for several years and is an easy succulent to grow.
Capsicum frutescens or annuum are short lived plants with interesting coloured pepper fruit.

Warning about Windowsills for plants

Sun can be strong through a window. Leaves may get burned if the window face south.
Windowsill plants can dry out because there is less soil, more sun or no natural humidity or micro climate to help.
Seedlings need extra care but as most windowsills are at an appropriate level you can see what is going on.
Take care not to dislodge plants from a windowsill the clearing up can be a pain.

Southern Facing Windowsills

Geraniums make good house plants and will flower most of the year given the chance and a regular light feed. Like many plants they are phototropic and grow towards the light. For this reason they need a quarter turn regularly to keep growth even. As windowsills may narrow you can try some of the dwarf or miniature varieties which I find fascinating (see the pink flower and variegated leaf in the background).
Stephanotis has a heady fragrance on waxy flowers and needs to be stood on damp pebbles to maintain humidity for best blooms. Keep well fertilised and provide some support for the climbing stems.
Cacti are often found on a windowsill and I would opt for one of the flowering Rebutia for its dainty appearance.
Cyclamen persicum are popular flowering plants for winter that need regular watering and humid conditions so avoid too much direct sunlight.
Cape Primroses or Streptocarpus are now available in many varieties and colours. The photograph shows an small flowered bicolour Blue Layla. Beware some Streptocarpus have one or two very large leaves that can be damaged by curtains and rough handling.
Windowsill Orchids or Pleiones make good windowsill bulbs as the name implies see Easy orchids from Bulbs