Most people can take an inch and a half in diameter with no problems (4-3/4" circumference). I'm experienced, and can take up to slightly over 2" diameter easily (2" diameter is 6-1/4" circumference). Much over that needs plenty of warm-up.
For me the ideal diameter is 1.25"-1.5", and the larger the toy, the softer the material needs to be. I just got a VIP Super Soft, and it's officially the largest toy I own at 1.75" in diameter - I'll need to warm up before I attempt it, haha!