The short answer is yes, obsessions and fixations are completely normal in toddlers. Between the ages of about two and four it is very normal for toddlers to become obsessed with a particular theme or topic. Toddlers thrive on repetition and routine, and as they grow out of the baby stage they begin to learn about the world around them. The world outside the comfort of their home can seem a very scary place, and so toddlers need a sense of routine in their lives in order to feel safe. Playing with the same toy or watching the same television programme over and over again gives children a sense of familiarity. It also gives them a certain amount of choice, and is a way for them to control their daily life and surroundings.
In addition, toddlers have reached an age and period of development where they have gained the level of understanding to allow them to see things from a different perspective, and to appreciate more than just their immediate surroundings. They now have the capability to imagine that they are a different character from a book or television programme, or they could even pretend that they are an inanimate object. I've noticed that my son often seems to spend a large amount of the day pretending that he is a train. He moves his arms around like wheels, accompanies himself with appropriate sound effects and insists that I couple myself on to him as we walk down the road. On other days he is a crane, and he uses his arms to move objects around the house. If I try to move something for him he will become angry and insist on moving it again himself. Behaviour like this shows that a toddler is developing his imagination, and learning how to act out situations that he sees both in real life and on a screen.
Most parents will have funny stories to tell about their toddlers obsessions, some mild and some more extreme. In the vast majority of cases it is something that is looked back upon with amusement, rather than a situation which led to any worrying developments in the future. Parent's stories can range from refusing to drink out of anything other than a favourite cup to spending all the hours of the day and night pretending to be an action hero, even to the extent of going everywhere in full costume.
Generally as a child grows up the fixation will gradually lesson and the obsessive phase will come to an end. Certainly most toddlers will have outgrown their obsessions by the time that they start school and are exposed to a wider friendship circle and range of experiences. Instead of worrying about a toddler obsession, it's usually best to embrace it and use it as a springboard for learning and further development.
There are some triggers and situations that might lead to an obsession in a toddler. For example, the repeated viewing of a particular television programme can be an easy way to entertain a child, but can then encourage a dependence upon the programme. Instead, it is important to give a child access to a range of different situations and experiences.
Parents should be reassured that toddler obsessions are completely common and normal, however if you have any doubts or feel that there is a cause for concern it is important to talk to your Health Visitor or doctor.