So, I play right handed. I read in another thread that playing with your left hand-thumb wrapped around the neck is a bad thing. Is this true, or only in certain cases? Should my thumb be placed in line with my index finger right on the back of the neck? I play lead guitar rock music if that helps.

Cheers, and search bar didn't come up with anything specific
you'll be able to play faster and easier with your thumb on the back of the neck instead of wrapped around. i do the same as you because i find it easier when i'm playing alot of chords or when i need to mute the low E string .

but do whatever works for you.
Quote by Martyr's Prayer
I got crap to do, okay? Counter-Strike isn't going to play itself.
All right, cheers. If I keep playing with my thumb wrapped around the back of the neck will it hinder my progress in improvisation and doing really fast solos, etc?
in gneerally it seen as bad technique so i'd assume it would hinder your progress, but i'm not really into lead guitar so i couldn't tell you from experience. the only problem i relaly have is that it's hard to play well on the higher frets with single cutaway guitars.
Quote by Martyr's Prayer
I got crap to do, okay? Counter-Strike isn't going to play itself.
Well it depends really on what you are playing. Sometimes it's easier to fret chords with ur thumb more hooked to give u better leverage to barre chords etc. ALso often u can use your thumb to fret notes on the sixth string instead of fully barring.

For lead work and the like its better to have your thumb on the back of the neck to assist in speed of movement and finger positioning on frets...

Anyone want to buy an Ibanez 7 string guitar?
This is a lie...no reason why...right from the outset
yes it is bad wrapping you thumb gives you less reach and speed but its your pref if you want to use it
i generally keep my thumb in the middle at the back of the neck, but the thumb does creep over the top for excessive bends as i think it aids in leverage. Quite a few of my pals only hook their thumb over the top when they're bending strings.
My gear:
Fender 50th anniv American Strat Deluxe NICE
Fender Eric johnson Strat SEXY
Gibson SG Special Gothic II RAW
Ibanez JS 1000 VERSATILE
Gibson Les Paul Custom OOH BABY
Mesa Boogie Dual Rectifier Head & Cab LET'S ROCK