I have been getting quotes to reshingle my roof. Some roofers said they wanted to put ice shield in the normal spot... the bottom. Others want to put ice shield at each edge of the roof, including at the ridge.

Is ice shield really needed at any other place besides the bottom edge of the roof?

I'll be interested in reading what my peers have to say on this. Ice shielding is only needed on the roof above the eave near the gutter. That is the only place where melted ice refreezes and requires the protection. Did the other roofers offer and explanation of why, other than their kid was going back to college.

Is ice shield really needed at any other place besides the bottom edge of the roof?

No the bottom edges is all you will need. Ice shielding is basically a doubling up on your tar paper and or first course of shingles. The old days metal flashing was used at the eves where the gutters are

Logan, the ONLY reason Ice damming is caused is because of POOR insulation at the eves. This allows heat to escape during the warmer part of the day and the evening it freezes up to create an Ice dam. With the proper conditions this repeats its self and can become HUGE in ice hanging off the gutters

Here's site I found last year to prove my answer about ice damming on an apartment complex and what causes it.
Ice Dams and Attic Condensation (http://www.statefarm.com/learning/loss_prevent/learning_lossprevention_icedams.asp)

I would ask the roofer how ice damming starts and what causes it to see if he knows roofing.

Thanks guys, that's what I thought. Some of the roofers said that sometimes in a severe storm, wind could possibly lift the edge of the house and water could penetrate.

As a wakefield roofing contractor (http://www.mbmcarpentry.com/services/roofs) the reason for more ice water coverage could be you have a very low sloped roof. I don't have all of the facts, but if you have a low sloped roof, and you're using asphalt shingles, having ice and water shield covering your entire roof deck would be a smart option.