Unfortunately, doping is still a high occurrence, weakly enforced problem in sports. One recent study comparing doping and socioeconomic variables points out that the WADA (World Anti Doping Association) testing protocols produce less than 1% positive results, but anonymous surveys and questioning puts the number of intentional intake at 39% (And likely higher actual value).
Another study on testing frequency shows that testing standards and frequency is vastly different from nation to nation.
Speaking at a personal n=1 level, I was a competitive cyclist (Cat 3, almost Cat 2 in the United States, so just below elite level), and I know as a fact that half the peloton at any given time was doping to some extent. Unless you are competing at a national event or in the USADA random testing pool, you aren't going to be tested.
Short answer, yes it is still a problem, and one that is not likely to be solved. Every time a new test comes out, new ways to get around it are created.