mass - Higgs field and masses of particles

Interaction of particle with Higgs field provides mass to the particles, then why still some particles are massless?

Answer

John Rennie's answer is good, but I'll try to explain intuitively why the symmetry breaking leaves some symmetry unbroken.

Start with a sphere. You can rotate a sphere in three independent ways—around the x axis, around the y axis, and around the z axis, if you like. All of these are symmetries of the sphere, i.e., they leave the sphere unchanged. These rotations are called $SU(2)$ [almost—there's a technicality that I'll ignore], and saying that an $SU(2)$ gauge theory has three gauge bosons (which it does) is the same as saying that a sphere can be rotated in three independent ways.

Draw a dot somewhere on the sphere. All three of the above rotations will probably move the dot, which means they are not symmetries of the sphere plus dot. But there is still a rotational direction that leaves the dot in place, and there was never any reason to prefer those other axes that don't. So forget about those axes and instead pick the axis of symmetry (an axis going through the dot and its antipodal point), and two other axes perpendicular to that one and each other. The axis of symmetry is the "photon", and I suppose you could call the other two the W⁺ and W⁻. This analogy is inaccurate in that the real electroweak gauge group is $SU(2)\times U(1)$, not $SU(2)$, and has four bosons, not three. But a sphere is much easier to visualize, and the basic principle is the same. Before the symmetry is broken (by drawing the dot), you can't be sure that any particular boson (rotational axis) will remain a symmetry (remain massless), but there will always be some combination of those bosons (some other axis) that remains a symmetry, and we call that the photon.