A lot of people still use EIG hosting without any problems. Your results will vary with them.
But other people have trouble with them. I believe the problem with the EIG web host companies is they overload their web servers with too many websites and customers and that causes website crashing and slowdowns.
A few web hosts that are owned by EIG that I can remember are hostgator and Ipage.
There's many more too.
If you want to find a non EIG host check out the hosting offers on
http://webmasterbabble.com webmaster forum.
That forum has lots of web hosting offers from non EIG web hosts to choose from.