Do eBay buyers ever ask you to sell outside of eBay?

Just got an email from a guy who offered to purchase an item I'm selling on eBay for about 30% more than the current bid. He wants to send funds via PayPal, then he wants me to cancel the auction. He made a very fair offer. He seems legit, has good feedback and thousands of transactions.

I don't sell a lot of stuff on eBay, so I wouldn't know if this is a scam or not. What are the risks and how should I protect myself if I decide to proceed?

If your item is sitting at $66 and he is offering another $18 or so (for a total of $84) it might be because he thinks it's going to go for more than that...say $100.  When they try that with me I usually just tell them to bid their max (the $84) and they will probably get it for less (or at the most, the $84).

They don't lose anything if they win it between $66 and $84, and you still win. If it goes higher than that they might continue on anyway. If they don't then you will be getting more than the $84 from someone else.

The only down side to you is if the auction bogs down and you only end up with the $66, but personally I'd rather go for the other bids. 

With a little over a day left your item is currently at $76 so my example above is fairly accurate I think !  ;

Have I ever posted a link to my eBay account?

No.

Sets of four have sold for $100 to $125. Singles have sold for $25 to $40.

If I'm not mistaken ebay also forbids you to exchange personal emails through ebay messaging which makes it hard to communicate with a buyer to arrange an off ebay deal.

Yeah, in order to provide the buyer with my email address I had to write it like this:  example (at) mywebsite.com

It happens occasionally. Seems like it is usually someone nearby but not always. In one case I had tons of miniatures from a closed miniatures store. There were these little porcelain vases. I had about 1600 of them. I was selling them on ebay in lots of 5 then 10 then 20, each time a slightly better deal because I wanted to get rid of them. I think the lots of 20 were $25.00. I would list 10 lots of 20 and the same person would buy them all. We finally exchanged phone numbers and made a deal off ebay for the rest of them. I think I had almost 1500 left at that point and she paid me $1400 for them. No fees. I do make sure to never make a deal in writing though. For me it's nice to avoid fees but not sure what the benefit is for the buyer.

Just got an email from a guy who offered to purchase an item I'm selling on eBay for about 30% more than the current bid. He wants to send funds via PayPal, then he wants me to cancel the auction.

Thee buy it now option is good but it defeats the purpose of the deal.  Getting out of Ebay's fees.