Great question.
- Electronic stability control (ESC) (required from 2009).
- Anti-lock braking system (ABS) (in most cars from 2004 due to EU regs, although not required in the US until 2011).
- From 2003 the IIHS started rating vehicles for: rollover risk, side impact, and frontal offset impact. So car manufacturers started improving their designs to score better in these tests. The whole "top safety pick" thing is an IIHS rating.
- From 2009 the NHTSA required a greater roof-crush load (3x the vehicle's weight, from 1.5x).
- Safety Cell improvements: Crumple zones are less likely to trap in the driver or front passenger's legs/feet during impact.
- Anti-intrusion bars: Are more standard. The IIHS tests kind of pushed them into mainstream.
- Additional air bags (side impact).
- Whiplash reduction seats and headrests.
Overall regulations aren't why cars are safer in 2016, consumer demand is. People decided they didn't want to compromise on safety, so as a safer and safer vehicles became available consumers flocked to them. Manufacturers had a financial interest in not only be safe but the absolute safest in the road, and that competition pushed vehicle safety forward.
Just for clarity, they did "frontal offset impact" tests a long time ago, small overlap however was a recent addition, you can see the difference between the two here[0].
So even in the early 2000s vehicles did improve for frontal offset impacts, they just improved further in the last couple of years with the small overlap tests.
[0] http://www.iihs.org/iihs/ratings/ratings-info/frontal-crash-...
One change you can see on the road: the new looong Jeeps. That's so the gas tank can be ahead of and protected in a crash by the rear axle, a safety improvement.