A couple years ago a friend of ours moved from a quiet courtyard apartment to a unit near a major city thoroughfare, resulting in many sleepless nights. At the time I gave her all the soundproofing tips I could think of (within their budget), including planting trees in front of their windows, hanging rugs/tapestries on the wall to dampen sounds, heavy drapes for their windows, earplugs, and even acoustic foam room tiling. Nothing has really worked, and she's just gotten used to the ambient sounds of traffic.
I might have to send her two links about soundproofing again. First, is an informative article from Wired titled, How to Soundproof an Apartment to Muffle Your Wife's Drumming. Some of the tips learned from soundproofing a room for a percussionist are: create a drop or false ceiling, mass-loaded vinyl flooring, replace hollow doors with solid-core ones, add acoustic seals around the edges of doors, and fill any gaps around windows or doors with flexible, non-hardening caulk. A notable point made was "soundproofing is not one thing, but a bunch of little things that add up, decibel by decibel."
The article also prominently mentions a damping material that dissipates sound in walls, floors and ceilings, called Green Glue. A water-based gel, Green Glue is to be applied inbetween drywall or subflooring, and can help reduce low frequency noise associated with exterior sounds by destroying vibration energy. The writer of the article noted above was able to significantly reduce their sound leakage with a $175 investment in 12 tubes to cover a decent sized wall. If you're fortunate to own your unit, this seems like a worthy avenue to investigate, while renters such as myself could discuss with their landlords, as it might not be a hard sell to offer adding a desirable feature to their property: a quiet space.