Andrew Ryan is voiced by Armin Shimerman. You might remember him asQuark or Principal Snyder or Nefarious. It can be difficult to recognize him the first two times he is heard, though - Shimerman absolutely nails that cultured fifties style of phrasing in the Rapture introduction and the second time he speaks is through a PA system. But he is clearly recognizable after he begins communicating with the player over their portable radio and in the voice recordings.
Frank Fontaine after dropping his Atlas guise is voiced by The OtherIroh.
Dr. Steinman is voiced by Peter Francis James, who can be often be seen on one Law & Order show or another as a judge.
Naledi Atkins' voice actor also voiced another female pilot whose plane was downed, namely Captain "Deadly" Pelayo from Modern Warfare.
The "Lady Smith" splicers and Dr. Langford are voiced by the same actress, whom you might know better as Wanda and Timmy's mom in The Fairly OddParents. She's also taken over voicing Cruella de Vil, Maleficent, and Lady Tremaine in recent Disney works such as Kingdom Hearts.
Sander Cohen is voiced by T. Ryder Smith, who might be best remembered as the villainous Trickster from the 90s horror film Brainscan, but more recently has been the voice of Baron Underbheit on The Venture Bros..
Within the first game itself, it's clear — and a bit jarring — that they re-used Peach Wilkins' (unnamed) voice actor for one-off character Charlie.
In Bioshock 2 the spider splicer model named the "crawler" is voiced by Sasuke or Ben depending on which one you're more familiar with.
The Japanese voice actors are more easily identified as Toshiyuki Morikawa is the voice actor for Atlas, Andrew Ryan is Unsho Ishizuka, Bridget Tenabaum is Mie Sonozaki, and Kaori Shimizu voice the Little Sisters. In other words terms, Shaggia Frost wants Jack to kill Sergei Smirnov while Aplodia Neuro tries to save Signum and Lain Iwakura.