Some "three-free" polishes include: Avon, China Glaze, Rescue Beauty Lounge, Elizabeth Arden, Revlon, L'Oreal, Rimmel, Lippmann Collection, Sally Hansen, Maybelline Salon Expert, Nars (newer formula), Spa Ritual, OPI (newer polishes are safe, but some hardeners use formaldehyde), and Zoya.
For a few of my favorite safe-polish picks, read more.
Nars Nail Polish ($16) has developed an improved formula. The varnishes are now enhanced with UV protection, have a glossier finish, and supposedly last longer without chipping (I haven't reached a verdict on this just yet). They are also free of formaldehyde, DBP, and toluene — which I think makes the smell less severe.
The polishes in the Lippman Collection ($15) are now not only free of DBP, formaldehyde, and toluene, but they also contain green tea and biotin (protein) to help your nails grow stronger. The formula dries quickly and has a really nice shine. I personally love the two new spring colors. Have you had the chance to check out Dream a Little Dream of Me yet?
Adorée Professional Nail Polish ($5) has more than 140 different nail colors in its range. While they are free of the "big three" polish no-no's, they do contain hardeners to help strengthen nails, and they claim to provide a high-shine finish.