Do any Buddhist traditions emphasize pilgrimage? I'm aware that other religions such as Islam have a great emphasis on pilgrimage.  Do any Buddhist schools or traditions also have an emphasis on pilgrimage and if so where do they go? I know that there are places with particular significance for Buddhism such as Bodhi Gaya and Buddhists do go there. But is that journey actually a significant part of their practice or tradition or is it just that it's personally inspirational to go.

From my own point of view I would love to go see places of historical and religious significance to Buddhism. If I did though I wouldn't view this as part of my practice as a Buddhist. It would almost be religious sightseeing.
There are four main places that most Buddhists visit at least once in their lifetime. According to Buddha's words in Mahaparinibbana sutta those are
Lumbini, Buddhagaya, Sarnath and Kusinara in Nepal and India.


  
  "These, Ananda, are the four places that a pious person should visit and look upon with feelings of reverence. And truly there will
  come to these places, Ananda, pious bhikkhus and bhikkhunis, laymen
  and laywomen, reflecting: 'Here the Tathagata was born! Here the
  Tathagata became fully enlightened in unsurpassed, supreme
  Enlightenment! Here the Tathagata set rolling the unexcelled Wheel of
  the Dhamma! Here the Tathagata passed away into the state of Nibbana
  in which no element of clinging remains!'
  "And whoever, Ananda, should die on such a pilgrimage with his heart established in faith, at the breaking up of the body, after
  death, will be reborn in a realm of heavenly happiness."
  DN 16
  


Pilgrimages however are not a significant part of the practice, but these visits can inspire us to put more effort into our practice. Some groups of people observe eight precepts and practice meditation as a part of the pilgrimage as well.   By showing reverence at these places, the person is able to purify his thoughts, speech and action. So by visiting these places with the correct mental attitude can help us in our practice as well.