In terms of the amount of designs you should be putting forward - that depends on what you have agreed with the client.
We at a fish in sea have fixed fee logo packages which outline how many initial designs the client gets and how many rounds of revision after that. Your initial concepts should be finished and polished logos - and presented in a high quality manner - don't bombard the client with all your workings, and pages and pages of ideas or have the company name duplicated in loads of different fonts!! They don't want to see that. You should be presenting them with (for eg) 6 well thought out, clean, finished and DIFFERENT logo designs that you would not mind giving to them straight away if they picked it outright. It can happen! DO NOT PUT IN ANY THAT YOU DONT LIKE JUST TO FULFIL THE CRITERIA! Thats just pure lazy, and the chances are that they will choose the duff design and you will be left thinking "Ohhh, I wish I didn't include that one"... serves you right!
The logo concepts should all differ from each other and communicate the brand in a different way. Don't put forward the same icon with a different font - give them variation and designs that all have merit in their own right. If you can't decide between 2 logos that look similar, then put it forward as an EXTRA alternative. Feel free to give the client more than 6 initial concepts (extra brownie points!) but only if you feel that the 7th and/or 8th one is as strong as the rest, but be brutal. Omit the weaker ones and put forward only your best. Occasionally you may find that you don't hit the clients needs with any of your first designs and the weaker designs you saved will be like gold dust to helping you come up with new ideas.