Heritage make a great Les Paul but the headstock is different and kinda ugly, and they're more expensive than a Gibson.
Tokai make a wide range of Les Paul copies, with the high end being superior to a Historic, to the low end being comparable to an epiphone (but probably better).
Tokai Forum has a lot of info about Tokais. Caution, Tokai also have a Korean brand which is actually quite nice and supposed to be better than an Epi, but is no substitute for a real Gibson (from what I've heard).
If used poses no problem for you Greco made an awesome series of replicas in the 80's called the Mint Collection. I have a 1982 '59 replica and it's incredible. 1piece mahogany back, 1 piece neck, Flamed maple bookmatched top (not veneer), Brazilian rosewood fretboard. Simply put, the materials used are better than on my 1981 Gibson Les Paul. The Neck pickup has a gorgeous tone and the bridge pickup (which was not original) is getting swapped out for a Nailbomb next week, when it finally gets here.
Burny also made a very good Les Paul replica. ( I use Replica instead of copy when i feel the craftmanship is on par with the original. )
Edwards (a subsiduary of ESP) have a line of fantastic looking Les Paul replicas including a Jimmy Page model that has been given the "relic" treatment. Fantastic looking. The Edwards logo is a little awkward looking though.
All the aforementioned guitars are Japanese and have the proper open book Les paul Headstock.
I have a Dean Evo that I really like that is very Les paul like without being a clone.
ESP's Eclipse line are a very nice pseudo Les paul as well.
My first guitar was a Columbus Les paul copy and it was... a piece of shite. I gigged with it for a couple years none the less!
