A landmark study by psychologist Daniel Wegner found that research participants ironically experienced a surge of intrusive thoughts, known as a rebound effect, when asked not to think about a white bear. They had a significantly higher level of thoughts about white bears when instructed NOT to think about them.Another study in cognitive science, conducted by Drs. Bonanno and Siddique (see ‘at play in the fields of consciousness’, 1999, Lawrence Erlbaum Publishers) found that a sub-group of people could effectively suppress thoughts, even following grief and loss, such as the death of a spouse. Known as dispositional repression, some people demonstrated a knack of not being inundated with intrusive imagery and thoughts. Intervening variables included the ability to distract oneself and receptivity to social support and interaction.

Both of these studies have important implications for people who suffer from intrusive thoughts. Intrusive thoughts are unwanted thoughts and images that can cause anxiety and distress. A global study found that up to 95% of people have intrusive thoughts, from the innocuous “did I remember to lock my door?” to more disturbing thoughts, such as “what if I run somebody over at a stoplight?”

Unlike regular thoughts, intrusive thoughts can be repetitive, uncomfortable, and are often difficult to control.
Clinical psychology research, including the studies mentioned above, indicate that not thinking about something requires first thinking about it. The harder we try to stop thinking about something, we may actually have a surge of thoughts about the undesired topic. Active attempts at thought suppression can have the opposite effect.

Recent research:
A 2020 study on patients with clinically intrusive thoughts (OCD) indicated they may place less trust in their past experiences, leading to greater uncertainty, indecisiveness and doubt. The findings showed that participants with higher levels of intrusive thoughts were less trusting of past experiences. They were constantly questioning themselves. As such, their environment felt consistently unpredictable.

So, what works to reduce intrusive thinking?
* Mindfulness
Research shows that mindfulness exercises can improve attention control, reduce anxiety and reduce intrusive thoughts. There are several variations of mindfulness (or mindfulness meditation). People can learn to reduce the significance of their intrusive thoughts by observing them without judgment. The simplest form of mindfulness is focused on paying attention to the present moment; sometimes by focusing on breath or a specific object.
*ACT-based psychotherapy
Another option, called acceptance mindfulness (ACT therapy) encourages you to look inward, noticing and acknowledging your thoughts and emotions, while choosing ACTION based on personal values (for example, if hurting someone is an intrusive thought, acknowledging that your personal values are not commensurate with that thought can help reduce discomfort and anxiety). 
*Distraction and social support
Having someone to talk to on a regular basis (reality check), whether a friend, mental health professional, clergy/spiritual guide, or trusted family member, can reduce the discomfort of having intrusive thoughts. 
* Managing stress levels
Experiencing a high level of stress can cause intrusive thoughts. According to the American Academy of Sleep Medicine, the genetic factors that cause sleep problems when some people are stressed are the same that can make people with intrusive, ruminative thoughts have a higher rate of insomnia. It’s not a coincidence that many people have intrusive thoughts at night, when they are presumably done with their busy day. This is one of the reasons why some of the most successful methods for battling anxiety and intrusive thinking involve curbing stress and working on effective sleep protocols.
*Therapy, with a focus on cognitive behavioral strategies
In addition to self-statements and personal mantras, I sometimes have clients make a checklist. Did I remember to feed the cat, turn off the stove, lock the door, take my medication? A visual reminder can be helpful.
* Reducing repetitive stimuli
If you are prone to intrusive thoughts, turning off your feed, or even taking a break from Twitter or other social media might be helpful. Social media facilitates intrusive thinking by sheer repetition.

Also see:
How to Reduce Anxiety on the Go: Strategies that Work
Mantras as Self Statements
Bonanno and Siddique, from the American Psychological Association: https://psycnet.apa.org/record/1999-02328-010