I use chords,double stops, implied chords, tapped and divided by octaves or 10ths, and double stops with false harmonics to imply a greater harmony....
I do primarily play solo (I was one of those solo bass looping kooks on the tour with Michael Manring and Steve Lawson), but I have, after considerable work, learned to incorporate chordal techniques into ensemble work as well.
As a learning aid I highly recommend Michael Dimin's book "The Chordal Way" (forgive me if I got that title wrong...) check out his forum here at TB for some great tips...and check his website for the book. It has a wealth of info on chords, and double stops.
On that same thought...I am working on a book myself much in the same vein: a chordal appraoch to bass. To accompany this I am compiling a "Bass Chord Dictionary" (geez, there's plenty of these for guitar....) I have 600+ chord voicings for bass, and the number is growing. Some are double stops which imply suspensions or chord extensions, and others are three and four note chords with extensions (7ths, 9ths, 11ths, 13ths etc.). Hopefully I will get it finished soon.
In usage, I have learned a great number of solo/chord-melody bass pieces including standards (Somewhere Over The Rainbow, Night And Day, The Lady Is A tramp), Rock Songs (Various Beatles tunes, "Stir It Up" and other B. Marley Tunes...) Show Tunes, Blues...even the Coca Cola jingle (which I segue into the pepsi jingle) and, of course, plenty of originals.
Chordal bass playing is tons of fun to mess around with, but truthfully, it is not appropriate for all styles of music. Nonetheless, by learning chordal theory (read: HARMONY) you learn more about music....and this has helped make me a better "traditional" bassist as well....
Max Valentino