There are some pots you can buy that do not have drainage holes in them so yes you can plant some plants in pots that do not have drainage holes.
But it's best to use pots that have drainage holes in them when planting plants because the holes in the pots allow excess water to drain out of the pot so that the plants do not get drowned in water.
The holes in the pots also let you know when you've given the plants enough water because when water starts coming out of the pots it means that the soil is soaked enough and you've given the plant enough water.
If you put plants in pots without holes you need to be more careful in how much water you give to the plants to avoid over watering them.