Most of what I know is that most condoms are made of latex, which a decent percentage of people have a slight to severe allergy of. So that's important to consider. Also, oil-based lubricants can damage a latex condom so only water- and silicone-based lubricants should be used with them.
But there's also polyurethane condoms that people with a latex allergy can use. It's just as durable as latex and can be used with any type of lubricant. They, however, do cost more.
I also figure that with nonporous, high quality materials (anything on the 10 material rating on EF) is safe for any condom. But that very porous and sensitive materials like jelly can be fogged or possibly stained by condoms that contain their own lubrication, powder, "flavor", or color. Not really sure. But those are the toys that it's most important to use a condom with.
Edit: Ok, did a little research and many sources suggest using non-lubricated condoms with jelly material specifically to help deter bacterial growth in the toy. Scary!