One license I think gets overlooked is the Mozilla Public License (MPL). I think it's particularly good for libraries and I've published some of my simple javascript code under it.
The interesting part about it is that it says modifications must be published, but that they are file based and not project or linker based. This omits many of the "onerous" (from the library user's perspective) restrictions of the LGPL, while still keeping the spirit of "this is free software, please give your enhancements to others to make the world better" which is sort of the whole point of GNU.
Note, though, that older versions of the MPL (before version 2.0) are incompatible with the GPL, so you end up with things like MPL/GPL dual-licensing. MPL 2.0 is OK in that regard, though I still prefer LGPL or GPL.
In many cases you can with LGPL, and you can with GPL if you explicitly add a licensing exception.
Also, regarding "use ... proprietary modules ... to better your program or library": depends on your definition of "better", but if that's one of your goals, then I agree that you don't want the GPL.
> Also, MPL allows static linking, the LGPL doesn't unless you explicitly state it.
The LGPL allows static linking, as long as you provide the means to relink with a modified version.
> For the record, would 'GPL + Linking exception' be incompatible with the GPL and LGPL?
Only in one direction. You can take code under the GPL plus a linking exception and merge it into a GPLed project, but the result will not have the exception, so you can't add proprietary code to the result.
The interesting part about it is that it says modifications must be published, but that they are file based and not project or linker based. This omits many of the "onerous" (from the library user's perspective) restrictions of the LGPL, while still keeping the spirit of "this is free software, please give your enhancements to others to make the world better" which is sort of the whole point of GNU.