A lot just depends on whether there is a lap belt or bar...the bars keep you from keeping them in a carrier, really. We've taken our son at 5 months to WDW and 10 months to DLR, and for most rides we had him on our lap just holding him both times. I can remember doing this for Dumbo, Small World, Peter Pan, Pooh, Pirates, Toad's, Snow White, and several others. If I remember correctly, he was sitting up okay by then, just a little wobbly. I kept him in the Ergo carrier for ones that I could, especially when he was smaller, like Buzz Lightyear (he slept the whole time), and TTA (WDW). The only one that I was a little surprised by was when they wouldn't let me take him on the Golden Zephyr at DCA when he was in the Ergo. They were like "you have to take him out and buckle him in". Um, he's 11 months old, that's not safe, CM. So we skipped it. Which is fine, but by comparison, it seems far more "dangerous" to take him down the little drops in Pirates and Malestrom, having to just hold on to him (he loves them, and we held on tight)!
In other news, I think 6 months is basically the perfect age to take a baby. We had a great time.