'to run across someone' means to meet them by accident.
- I hadn't seen Gloria for ages when I ran across her in the supermarket.
- I ran across an old friend in town today. I hadn't seen him for ages.
'to run around' means to be very busy doing lots of things.
- I'm always running around trying to get everything done on time.
- I spent all morning running around trying to find the things you needed.
'to run away' means to leave, often secretly, because you're unhappy.
- He was very unhappy in boarding school and ran away twice.
- She ran away from home at sixteen and went to live with a friend in London.
'to run down' means to move quickly to a place in a lower position.
- When I called her, she ran down so fast she nearly fell.
- When I heard the news I ran down the street to tell Lily who lives at the bottom.
'to run down' also means to deliberately reduce the size of something, for example stock.
- Stock is very expensive. We're trying to run it down to a minimum.
- They are running the company down by not replacing people who leave.
'to run someone down' means to hit a person when driving your car.
- I was crossing the road when a car nearly ran me down.
- She's in hospital after being run down by a car on Market Street.
'to run into' problems means to meet or encounter difficulties.
- We ran into huge financial difficulties when the construction went over budget.
- The company has run into difficulties since the introduction of the euro.
'to run into' something when you're driving means to hit something.
- When I was parking, I ran into a post.
- I didn't brake quickly enough and ran into the car in front.
'to run off' means to escape or leave a place quickly.
- The boys took some sweets from the shop and ran off laughing.
- She waved goodbye and ran off to play with her friends.
'to run off with' something is to steal it.
- They hit the man and ran off with his wallet and mobile phone.
- The financial manager ran off with half a million of the company's money