Does anyone know what the highest conversation checks are for the Speech and Barter skills?

Skill points are limited in the game so I'd rather not raise them any higher than necessary.

What are the highest checks you've seen?

I saw a few speech checks around 75-80 though most are 50-60 or lower, and the only 100% speech checks where in the very final area of the game and are unnecessary. Barter checks are usually in the mid 40's-50's or lower, but there's a few in the 65-80 range too.

Okay, I can easily get them both to 50.

I forgot to ask about Explosives and Repair.

How much Explosives and Repair do I need to disarm traps like Land Mines and Rigged Shotguns?

Don't think you need explosives to disarm things. As for repair, I had mine set at 50 and I could handle everything, so some number lower than that.

Highest speech I've ever encountered as an 85 at the very end.

Okay, I just started a new game and did some testing in Harland's room at the REPCONN Test site. Here's a list of what I found there.

22 Repair to disarm a tripwire
23 Repair to disarm a bear trap
45 Repair to disarm a rigged shotgun
55 Repair to rearm a bear trap

28 Explosives to disarm a concealed mine
45 Explosives to disarm a rigged terminal

At end game there is a 100 speech skill check if you are siding with the NCR faction...

So far I've seen both 90 speech and barter checks. But I am just barely scratching the surface of New Vegas itself.

The game is mighty big, and even to this day I haven't seen/done everything in FO1 and 2 because of their scale. It's not likely I will ever see/do everything in New Vegas, either.