Does Agent A give written permission? Does Agent A's SELLER also give consent? 

IDX/Broker Reciprocity does just that - present cooperating brokerage's listings with attribution. The problems start when you represent them 'as your own' which I'm pretty sure is not your intent.
Here's another question: why not spend that time and those resources prospecting for your own listings and buyers . . . you can certainly keep inventory in your head for buyers, but you're helping the seller and seller's agent more than yourself marketing their listings.

I know you can do it if agent A is under the same brokerage as listings belong to the broker and not the agent.  If you are not under the same brokerage, I would ask for permission. 

Not without their permission and making it clear the listing belong to them, not you. And I would check with your Board/MLS on any rules/wording.

With their permission unless your IDX provides you with the correct verbiage. In coop with the MLS etc .......

Investigate how to present an IDX & all that works with it. Most agents don't understand how the whole thing works. Educate yourself & you'll have a boatload of listings to advertise.

I have had agents ask me permission to post on criagslist and other sites, in the hopes of getting buyers interested in the property. 

I think as long as permission is granted, it is a positive thing.

Lots of agents host open houses for other agents as well.  Of course, permission always received for that as well

Your question has received many quality answers. Key is not to make the listing appear to be yours and have the agreement of the listing agent either directly or through your mls.

I don't know about your area, but in mine, if you work for the same brokerage, yes.  If not, no.  

Remember listings belong to the brokers, not the agents.

IDX does that for us, Gary.

Other than that, here in NC or SC, you have to have the BROKER'S permission to list another agent's property.

What Candice A. Donofrio said.  You need their permission to do so and that is an uphill battle.  I won't even let other agents hold my homes open, certainly won't let them advertise it.

IF it was YOUR listing would it be ok with you to have another agent stuffing mail boxes with your clients house?

Know the laws of your state, the rules of your association and the strength of your brokers backbone. Most will throw you under the bus.

It's all about written permission of the seller and listing agent's broker.

Zillow gets paid to do that. 

You should have permission. Include a link to entire mls is best.

With their written permission - yes.  Always make sure you are in compliance with the local rules as well. 

Not unless you had that agent's permission.

Only with permission of the other agent's broker.

Only with written permission in my locale!

Read every word written by Candice A. Donofrio and when you finish, read it again....repeat until you have it permanently carved in your memory.... learn to market and make your phone ring and you'll never need to tread in that gray area....

I agree with what Candice A. Donofrio said. 

You need to have a conversation with your broker.

I think that is a question for your board.  I have used other agents listings in a publication, but have asked their permission in advance to include both the listing and the image.  I know you can definitely NOT use an image without the permission of the agent and/or photographer.

Great question and asnwers. Good luck. 

Good answers are here. I hope you find the best one. 

Gary Eberhart No, not unless you have permission to do so.

It may be, with permission of the listing broker and agent.

Good luck. You should make sure you get permission and mention the name of listing agent. Check mls rules, get agent's permission and check state laws. 

Candice has given you good advice.

Gary Eberhart - if it is from your own firm, it should be. Or you can promote HUD listings, too.

If they give you permission and you indicate the listing brokerage, but check with your local licensing laws and your broker before doing so.

Without written permission one can get booted out of the brokerage,

  Candice A. Donofrio has the answer. 

It depends on your state law and the permission of the seller, the listing agent and his broker and yours.

I agree with the answers stating you need the broker's or agent's permission. I wonder how often agent B would become the buyer's agent.

as others before have stated, ONLY with permission, and recommend getting it in writing.

No!!! That would be hijacking a listing. You need express permission from the listing agent. If you don't, you'll be in big doodoo and perhaps violating the code of ethics.

Read up on IDX

Of course, with a permission of that agent.

Does the listing agent and seller give permission?  If so, then yes but if not, there is an issue. We have broker reciprocity with advertising all MLS listings in our website, including those of other brokerages, but in order to list the property without the information on the listing brokerage, the listing agent needs to provide the okay.

You need listing agent's permission; listing agent needs seller's permission (especially photo's - privacy). I think maybe if you said something like: 5 homes available on ABC Street, and provide MLS link? 

You'll have to read the rules and regs of your MLS and talk to your broker.  One agent, in our very own brokerage, took my listings along with other agent listings in our office and advertising them on Craigslist.  One of my sellers saw it and questioned why it didn't have my name on it.  Simply said, he is no longer with our company.

Not without the consent of the listing agent and the Seller. That would be inappropriate and misleading.

Gary,

Candice A. Donofrio is channeling my answers, or I am channeling hers.  The bottom line is we are both right! 

Whether it is okay or not...its being done

With their permission and crediting it to the listing agent yes.

Also, your brokerage likely allows you to advertise all their own listings without the agents consent...but it depends on how you're presenting the homes.

If the listing belongs to the brokerage you work for yes; otherwise no.

You can't do a specific listing without permission... and get it in writing even in your own brokerage it seems like common courtesy.  Gary Eberhart 

Get agent approval I think

Only with written permission.