Generally for a web design I will offer 3 - 5 initial designs, then the client chooses which to progress with and which parts of the other designs they like, and then a new design is made bases on that and then usually one more iteration to finalise things. It's usually never that simple though!
I usually give a maximum of 3 design options. It's better to understand the kind of design the client likes by asking him his favourite sites / logos or whatever design solution he is looking for. Understand his taste and likings and design something around it. By doing so, I have always succeeded in selling within 3 design options. Just create the WOW factor. Making lots of options may confuse the client.