For i in 1-100 do

Basically count to 100 and perform an operation each time i increases.

for ((i=1; i<=100;i++))
do 
  echo $i
done

for loop 1 liner

for ((i=1; i<=100;i++)) do echo $i ; done

While true (Execute forever)

Handy if you just want a script to run and repeat the same thing over and over again. Doesn't stop till you kill it.

while true
do
  echo "Repeat till infinity"
  sleep 1
done

While command is true

The following will execute the loop as long as the command in the () returns true. Once it returns false, it'll stop the loop

while (fping incredigeek.com | grep alive); 
do
  echo alive
  sleep 1
done