Bob Dylan and Joni Mitchell are the most influential singer/songwriters. Pretty much everyone you hear of these days will claim one or both of them as influences. In the 80s, folks like Suzanne Vega, Michelle Shocked, and John Gorka got quite a bit of mileage on the scene. Ani Difranco is the most popular these days. Some other notables I recommend are Lucy Kaplansky, Greg Brown, Dar Williams, and Nerissa & Katryna Nields.
Instruments of Choice:
Most Contemporary Folk Singer/Songwriters center their songs around acoustic guitar. Since Bob Dylan went electric at Newport Folk Festival in 1969, though, it's become less rare to hear folks in this genre experimenting with electricity. Suzanne Vega may have made the most daring exploration with her 99.9F Degrees CD (A&M 1992). Other instruments include everything from horns and strings to various types of drums. The didjeridoo shows up a lot, as does hammered dulcimer.
Bob Dylan - The Freewheelin' Bob Dylan (Columbia, 1963). Joni Mitchell - Blue (Reprise,1971). Phil Ochs - All the News That's Fit to Sing (Elektra, 1964). Greg Brown - Covenant (Red House, 2000). Dar Williams - The Honesty Room (Razor & Tie, 1993).
Singer/Songwriters tend to have their feet in all types of Folk Music. Some, like Lucinda Williams and John Denver, have clear country music roots, whereas folks like Phil Ochs and the Nields Sisters have roots in more traditional Americana. Meanwhile there are Singer/Songwriters like Michelle Shocked and Ani Difranco, whose influences are clearly broader and range from rock to blues and world music. This is the most versatile genre and therefore can be the most fun to explore.