You are going to get responses listing almost every current popular handgun manufacturer out there. But from my experience, when it comes to reliability of feeding many different types of ammo, you can't go wrong with a Beretta 92FS (9mm) or 96 (.40 S&W), a Springfield XD (any caliber), or Ruger P series. I hear great things about Sig Sauer, Glock and HK but have never owned any of these. Brands to stay away from in my opinion, based on personal experience, are Taurus and Kel-Tec.
You will get more opinions than you know what to do with. But most of the big name brands are turning out very reliable autos these days, so stick with them if budget isn't an issue and out-of-the-box reliability is. (Ruger, S&W, Colt, Springfield, Beretta, Sig, Glock, HK)