I will try to cover the main issues that occur for observant Jews when dealing on ebay, whether buying or selling. The main issues are buying and selling on the Sabbath, when the actual sale occurs Halakhicly and what would be forbidden to sell.

Firstly we must understand when the actual transaction takes place. The traditional methods of acquisition are no longer prevelant, and most transactions take place electroniclly. The Talmud in Tractate Baba Metzia (74.) teaches a concept called Setimta, which means that any law that is understood and practiced between Merchants is valid and binding Halakhicly (note 1). This was explained by the Maimonides (Zechia U'Matana 1:15) to include any law that was decreed by the local government regarding money matters. The Shulchan Aruch (Choshen Mishpat 201:2) repeated this and specificly states that any form of acquisition commonly practiced has full effect.

That mentioned, whatever law applies legally will have effect on ebay Halakhicly as well. When buying something on ebay, in reality, you are not buying directly. Rather, eBay/Paypal is the middleman in all transactions. When a buyer pays, the money does not go directly to the seller, it stays in your paypal account until you (the seller) transfer it out. During that time, the money is not in your hands, even though you are in the position of retrieving it when you want. As for the buyer, he does not own the item until he pays and gives over the money to paypal.

That being said, when your eBay store is open on the Sabbath, even if someone is buying on the Sabbath, he is not buying directly from you, rather through the middleman, Ebay/Paypal. Same is true when a buyer buys from a seller in a part of the world where the Sabbath arrived already, even if the seller is Jewish as well, it is permitted, since you are not buying directly from him, rather through eBay/Paypal. You can even bid on an item that ends on the Sabbath, as long as you don't pay on the Sabbath, because the acquisition doesn't take place until you pay. The only thing forbidden for a seller to do on the Sabbath is to transfer the money out of his Paypal account, as by doing so he is completing his side of the transaction.

An easy way to look at it is, that Ebay is your salesman who you give over your inventory to and notifies you when something sells.

An outcome of this Halakha is that you have full responsibility over the item until you complete the transaction by removing the money from Paypal. Once you ship though, it is out of your responsibility and in the responsibility of the buyer. This is true because the Mail Carrier is a "Messenger" (שליח) of the buyer. Whenever a receiver agrees that something be sent to him with a certain person or company it is his full responsibility if it is lost or stolen, and if he wants to insure himself, that's his choice.

Regarding items that would be forbidden to sell Halakhicly, truth is there is very little that is forbidden. The source of the prohibition in most cases is the verse "Though shall not put a stumbling-block before the blind" (Leviticus 19:14). This verse was expounded to include putting any temptation in front of any man that can lead him to sin (Maimonides comm. to Mishna, Shevi'it 5:6). This is understood to include anything that would be forbidden for you to buy, so it would be forbidden to sell idols etc. But the Halakha states, that any time that the buyer can acquire the same item elsewhere, it is permitted, as he could have done it without you (Abodah Zara 6:). From the words of Nachmanides (quoted by the R"an first chapter Avodah Zara), it can be seen that this is completely permitted (note 2).  

Even in situations where that specific item is not available elsewhere, if there is a possibility that it will be used in a permissible way it is permitted (Ritva avodah zara 63:). For example if you are selling immodest shirt, and the buyer can wear it over a long shirt etc. it is permitted (Yehave da'at 67). Same would apply to selling books that contain heretic teachings, since they can be used by someone to disprove it and prove the truth, or kept as a collectible it is permitted.

What is forbidden though, is to have benefit from idolatry, but only the idol itself, surrounding objects, such as a cross would be permitted, as they are not actually worshipped (Shulchan Aruch 141:1 (Ra"ma)). There are other less practical prohibitions as well, such as benefiting from a mixture of meat and milk. 

The Halakha here is following the Customs of Sephardic Jews, based on the rulings of the Chief Rabbi of Israel, Chacham Ovadia Yosef, under the guidance of Rabbi Shimon Alouf, Rabbi of the Egyptian Community in NY.

Notes:

1. If Setimta has effect Biblically or only Rabbinically is a dispute between the Chatam Sofer and the Netivot Hamishpat
2. Tosafot (Shabbat 3.) is of the opinion that it is forbidden Rabbinicly 

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