So I've just about maxed out all of my skills, with about 6 more points to go. Will I still be able to play afterwards or will I be stuck on the level up screen?

This bug was fixed before New Vegas was in development, so No.

Ok good to know, thanks.

no he wont be able to play afterwards or no he wont be stuck? you have to be more specific in your answers.

It seems the OP has his answer. Curious how you don't seem to get it though.....

I didn't even know it was fully possible to max all skills (without temporary skill books and armor).

The only things I can think of are using "Tag', full Intelligence, skilled, and educated. I doubt you can even reach 100 with those, though.

By the time I hit level 50, I'm maxed on most things (but only about 30 on guns and explosives, and about 16 on melee weapons).

You'll need to use TAG, Educated, Skilled and get your INT maxed ASAP and collect skill books, you nailed it. My last character didn't really get a lot of the skill books, so I wasted a lot of points. I'm more actively looking for them now. Gonna have to use a Stealth Boy to steal the book from Ranger Andy this time. I did remember to take Educated early and took Skilled as a trait. I'll be closer to maxing out this time.

Yeah I spent hours collecting skill books...

I hit the max in my last character right at level 50. I had 10 INT (9 until I got the implant), the Skilled trait, and took the Educated perk when it showed up. Didn't have to take the Tag! perk.

I liked having all the skill check skills (Medicine, Survival, Science, Speech, Barter) maxed because I was roleplaying an intelligent polymath, but towards the end I was actually kind of bummed, because my character lost definition, being maxed out on all skills that I'd possibly use more than once made the ones I actually specialized in seem less... special. I think there should have been some adjustment when the DLCs increased the level cap (and therefore the skill points available) by 66%.

Yeah, I'm at level 45 and I'm already maxed out... I was all excited at first, and then I now I'm kind of bummed as well. However, it is nice to pass every single skill check though.

I thought that skill books aren't permanent. I like having permanent maxed points.

Skill books are permanent magazines are not.

I'm an idiot.

Just pick up the book with Z key ( don't hit E ) carry it into the bathroom or some corner..drop it on the floor..go sneak..if hidden..steal !

You can do it with anything you want to steal.

Took both books in Sloan while barracks was full ...nobody noticed.
Cleaned out Van Graffs...just carried everything to the bathroom and stole it.

If you have OWB you can also make books....