Traditionally, most fantasy miniatures represent warriors, wizards and other combatant or adventurous types, and even then only people. This leaves many of us gamemasters want more miniatures, both for scenes taking place in the middle of crowds or where larger, more exotic weapons are used in combat. There are some such items various manufacturers are producing, but mostly they are metal miniatures, and many prepainted miniature collectors want to stay away from those metal ones. While I'm going to give you a few links at the end of the post, I'm now paying attention to what you can find from toy stores or scratchbuild simply.
Here you can see a war elephant. This elephant is a toy elephant just as it is (except for it's howdah), such Horses of the chariots are toys as well. I picked a packet with 7 (IIRC) horses very cheaply, painted them and now I have a bunch of horses available for rpg use - and these ones ended up to pull a wagon and a chariot. The elephant is a product of Schleich.
Howdah is quite simple; I've checked that a 1" miniature base can fit in, or two if the miniature on the base doesn't take much room. Another mini can be placed on the elephant's head. I've used a ball-point pen to create the plank-like surface (by pressing hard when drawing) for the sides of the howdah.
The chariot has a bit more complexity - years ago I made some casts of a single cart wheel I made but then didn't have time to model anything from them. Now I dug them up. Solid cart wheels are easier to make just from 1mm (1/25") or a bit thicker cardboard, creating wood structure as described above and adding two extra planks and a little drop of PVA glue in the middle of it.
The little wagon is quite simple, it's created from cardboard and wire. And cast wheels, but these wheels are really quite easy to make. Below you'll see more photos about all these items.
If you want to stay out of toys or want to avoid even little work with your minis, then you are probably interested in what's available as ready miniatures. There are two chariots available in Mage Knight, both a bit more exotic design. Unfortunately they are both out at T&T, and while they weren't out I couldn't buy them because overseas mailing costs for large items were very high. If you want to see the items (and add them to wishlist or seek for them elsewhere) they are here: Immortal Charger and Altarean Ram .
I don't know of any prepainted 35mm wagons or war elephants - if you know of any, please let me know. There is Tundra Scout in DDM though, a frost giant riding a mammoth which might be modifiable, but you might do better if you use a toy elephant.