Everybody knows about the Burke-Gilman. Here is the wikipedia entry for the Burke. Here’s a link about the trail’s history from the Seattle website. It’s a nice ride, but watch out for pedestrians and skaters. There is a missing link in Ballard between Fred Myers and Market Street. (They need to just get over it and build the trail – it can’t be any worse than the Duwamish Trail by the glass plants on West Marginal Way. ) Eventually it is supposed to go on to Shilshole and Golden Gardens.
Here’s the Seattle page describing current plans.
At the other end it connects up with the Sammamish River trail. There is some dispute about where one ends and the other begins but at Blythe Park in Bothell there is a Burke Gillman trail sign. The Sammamish River trail goes on to Marymore Park in Redmond. From there you can pick up the SR 520 trail back to Bellevue or the unpaved East Lake Sammamish trail to Issaquah. Once that’s paved you’ll be able to ride on trail all the way from Puget Sound to the Cascade foothills. (Actually you can pretty much already do that – and in a more direct route – on the I-90 trail, but the Burke – Sammamish combination will be much cooler.)
Watch out for speeding / stopsign tickets in Lake Forest Park.
Leave the Burke at 20th for the Ravenna shortcut .
Leave the Burke at the Freemont Bridge for the waterfront via either the South Ship Canal Trail or Dexter.
Leave the Burke at Juanita Way for the North Lake Washington Loop.
Here is the Burke Gilman page from the king county web site.
Here is a 2013 plan for redeveloping the UW section of the trail (big pdf).