First off, this isn't legal advice and I'm not a lawyer.
There are tons of opensource licenses: http://www.opensource.org/licenses/alphabetical, and you have many different licensing options. Here's a super brief run down of popular license options... I may have gotten some details wrong.
GPL doesn't allow your code to be used in a project that is closed source (proprietary). You should only use the GPL license when you want to force anyone else who uses your code to have an open source project as well. Specific to your question, licensing your engine under the GPL would probably turn a lot (the majority) of people away from using it.
LGPL allows your code to be used in a project that's closed as long as they don't directly include your code in their project, but link to your code as a dynamic library instead. The project maintainers are also required to make any changes they make to your library available (so any bug fixes, etc need to be made available as open source). The linking issue has important consequences -- afaik technically you shouldn't be using LGPL'd code in a closed project on iOS for example, since they only allow static linking.
BSD allows your code to be used in a closed source project as long as proper attribution is maintained. There are some other specifics as well that try and absolve the author of the code from being liable for its use. This is a much more liberal license than any of the GPL ones.
MIT is very similar to BSD. Both BSD and MIT basically allow anyone to do practically whatever they want with your code. They aren't obligated to make any changes/fixes they apply back to you and can include your code in their project in any way they deem fit.
There are tons of other licenses. I suggest you check out the Apache license, Mozilla license, and the zlib license as they're in common use as well. Also check out the WTFPL :)
There are also important details between license versions, especially with the GPL licenses... so make sure you read up on those before choosing between LGPLv3 and LGPLv2.1 for example.