Halflife did not ship with CTF already set up. You need a mod that supports the gameplay. Of these, there are several
And I'm certain there are others, but most of them are kinda stupid sorts of things, like Snow Wars and Monkey Strike.
TFC has a very malleable entity system that should allow you to create CTF gameplay any number of ways. It's still class based though, so if you prefer making people just pickup their weapons you won't want that.
AG is a good choice, in my opinion, for designing a CTF map in HL with standard HLDM weapons, but the community for the mod is mostly just the supernasty players that like to duel each other so don't expect much play.
I'm not sure what state OpFor is in right now, I even heard somewhere you can't currently play OpFor CTF online somewhere, but I think it's a lie. There's probably not many games going. It has all the OpFor weapons and I think the flags work as you are describing "Traditional CTF." There's also powerups that you can put in the maps, which recently were also made available to plain OpFor DM maps, which was really too damn late for any mappers to care unfortunately.
If you aren't asking about HL at all, but rather about CTF in UT, then you gotta say exactly which game you want help with specifically, or no one will know what you're talking about. Don't expect to get answers, as this is a HL site.