Should I use a sequential duplex receptacles or should I use multiple duplex receptacle circuit. I am setting up recepticles in the basement of my house.

Maybe I need to explain more. I have an electrical 'how to' book that. It explains how to setup duplex receptacles two different ways. One uses three wires and one uses two wires. What it does not tell me is the best way to do it.

I'm still confused.
Does the 3-wire method describe split-wiring the duplex receptacles? If so there is no good reason to do this for general use receptacles.

Are you referring to wiring in parallel vs. series? If so I prefer parallel -- it's a little more work, but if an outlet malfunctions, the rest of the ones down the line will continue to work.

It involves pigtailing the hot neutral and ground wires in the box to attach them to the receptacle.

It's ALL "parallel" wiring. That method is simply pigtailing.

There is NO "series" wiring in AC building wiring. Alarms are many times wired in series.

OK
I am going to go with the 2 wire method since there is no special reason to do otherwise.

Does a bathroom have to have its own dedicated 20 amp circuit for outlets by the sink. The reason I ask is because I am adding a bar sink right outside the bathroom wall and I would like to use the same circuit for the Microwave, small fridge and counter top outlets.

My mistake Stan, thanks for clarifying...

I suppose the use of a neutral wire eliminates the possibility of wiring in series?

I know a lot of folks use the term "series" to describe receptacles wired to the screw terminals. If you consider each wire individually they are technically wired in series, but regardless of how it is wired, the circuit itself is wired in parallel.

This is why I do not like to see the word "series" used for any kind of building AC wiring, it is too easy for a DIY to get mixed up.
I have actually heard of DIYers wiring recessed lights truly in series. They wondered why the lights were so dim compared to the rest of the house.