I would go as close to their 3rd birthday as you can, so they're still free, but can definitely enjoy it more than a 18-24 month old can. I've taken my now 5, 4 and 2yr olds 3 times over the last 3 years. The first time our oldest was 2yrs 4 months and the 2nd was only 14 months old. Our last trip the now 5yr old and 4 yr old absolutely loved it, and the youngest who was 18 months at the time also had a blast. For a 2 year old, if they're into the characters, it's great. My youngest on the last trip went crazy for all of them, but I remember my oldest was a little hesitant at first before getting into it.
It also helped for the youngest her older siblings would watch ride videos and listen to the Disney World sound track over and over in the car before she ever went. Having them exposed to that beforehand definitely increases their enjoyment when they finally do go. My oldest would dance around to 'Yo Ho' before our first trip and his mind was absolutely blown when we waiting in line and the song came on.
So Pros:
Watching them enjoy WDW is awesome. It really brings a whole new level to visiting the parks, and we honestly wouldn't go without our kids after experiencing it with them.
Obviously being under 3 means almost everything is free, including all character meals/buffets. - We took huge advantage of this when we had 2 under 3.
Getting them hooked early means even more of a reason to go back to WDW sooner rather than later.
Riderswap is great for still being able to go on the bigger rides.
Cons:
Waaay slower pace. Don't expect on going on much more than 4-6 rides per day. Our general schedule with a 2yr old was knocking out our 3 fast pass rides before lunch. Nice quiet sit down lunch/nap time after. You can usually get away with letting them nap in the stroller while you walk around the park, but some people insist on going back to the hotel and pool for the afternoon. You'll find out what your kid will let you do. And then trying to go on a couple more rides/dinner in the evening. We kept our rides to whatever we could get fastpasses for to keep the line waiting to a minimum. You also might find that it takes so long to get around with a stroller, diaper bag check, etc. that Park Hopping might not make sense.
Fireworks. My oldest was/is terrified of them. We found this out the hard way and I had to spend 15 minutes with him in the bathroom covering his ears til the show was over. Definitely try to gauge before you go if they'd like it before getting stuck in the middle of the show and nowhere to escape the noise.