When Morpheus offers the pill choice to Neo, they are still in the Matrix. That leads me to belive that none of the pills are real thus having no particular effect in the real world. Was it some sort of placebo effect that freed Neo from the Matrix or do the pills have an actual effect?
The pill helps the crew locate a person:
The pill is actually a tracing program that disrupts the carrier signal of the pod-human's mind, making it possible for a hovercraft operator to locate the pod that holds the human, and sending commands that force it to go offline and awaken its inhabitant.
This is confirmed within the script (pg 31) (thanks to cde for pointing this out):
MORPHEUS: The pill you took is part of a trace program. It's designed to disrupt your input/output carrier signal so we can pinpoint your location.
So it actually has a function beyond a symbolic choice. In fact, individuals who have been freed from The Matrix are called 'Redpills'
The Blue pill, according to the same page cited above, is thought to contain a 'reset' function which makes the person forget their conversation about the Matrix and continue to lead their normal life in the Matrix. Similarly, 'Bluepills' refers to people who haven't been freed. However, according to the webcomics, Bluepills do remember their conversations (kudos Richard).
As an aside, prior to The Matrix, the idea of a red pill was referenced in Total Recall where a red pill is offered to Quaid as "a symbol—of your desire to return to reality"
This was answered in a rare 2001 webchat with the Wachowskis:
Jose: What kind of drug does the red pill contain?
WachowskiBros: It’s like a computer virus that’s meant to disrupt Neo’s life signal so that they can pinpoint where Neo’s body is in the power plant..
This tallies very nicely with Morpheus' description from the original Matrix film
Morpheus: The pill you took is part of a trace program. It's designed to disrupt your input/output carrier signal so we can pinpoint your location.
Per my answer here, within the film canon the precise nature of the "blue-pill" isn't described although we can infer from the quote from Morpheus that it's a sedative;
You take the blue pill, the story ends. You wake up in your bed and believe whatever you want to believe. You take the red pill, you stay in wonderland, and I show you how deep the rabbit hole goes.
In the canon Matrix Comic "A life Less Empty", the main character; Tiera took the blue pill. She clearly recalls discussing the nature of the Matrix with Morpheus but then returns to her normal life. The 'splinter' remains in her mind (causing fits of depression and suicidal tendencies) but without any possibility of escape. There's no indication that the pill had any other affect than simply knocking her out.