Most sippy cups have BPA and I have been told Avent is one of the worst offenders. The only way to be sure you're getting a safe cup is to only buy those labeled BPA free. Born Free is one brand I know is BPA free. I had a tough time finding these, but just stumbled on them at "Creative Kid Stuff" of all places! They're a little pricey at about $30 for three small ones. But it's worth it.
On the same topic, I also discovered many of the plastic mock-melamine dinner plates, bowls etc. have BPA in them and just got through getting rid of everything, even my kids' character plate sets for brand new china plates etc. Be sure they're American made, and labeled lead-free. Gibson sells china that has been inspected and labeled safe. Also watch out for the cheaper silverware, which much that has been manufactured in china is not pure.
I had a set from IKEA that I had to dump after it started rusting. Though it was supposedly stainless steel, the interior was not and had traces of lead and other dangerous metals in it. I now have all new stainless steel that has been labeled genuine stainless steel.
This is all a real bummer isn't it? But who wants brain damage and health problems?