IMHO..unless you have a particularly close relationship with the child.. a small but thoughtful gift from you is sufficient.  I think it's nice to show interest in the kids by getting them something from you.  

If you do not have a good relationship with the kids? I wouldn't put on some pretend show with presents (not saying this is you.. just putting it out there in general).

I don't think you should necessarily be added to dad's/santa's card.. unless you are prepared to share in that cost.  

just further, dad should not be pooling money with mom so she can put some huge pile under her tree either.

any gifts bought were "us" gifts so I let the Mr do the buying. 

Wheee he saves money the whole year for Christmas.  Gifts, tree, food. Gifts to other family. HE should be buying the main gifts.  If you want to get something little. It's ok 

I usually give something around the same value as i give my niece and nephew to the 2 that live locally, and i'll get similar for the ones who live out of state if they are here for Christmas. If not, i don't mail gifts. 

I really wanted to give those "domestic t3rrorists" some lumps of coal but I let the dude take the lead and if he only spent $xxx for my kid then I spent 75% of what he did on mine for his 2. 
 

I gave him the cash and let him put it towards Christmas gifts. 

I used to buy SD13 all sorts of gifts, especially when she was little. Clothes, toys, etc. you name it! Not just one, but it was a considerable amount too. Well over $100. I started realizing she was unappreciative of all the gifts and wouldn't take care of them at all. For example, I got her a Polaroid Instax Camera. The film was thrown all over her room and the camera was broken within a month. Clothes were never worn or "got lost" at BMs. 

I quit buying a few years ago and DH just says they are from "both of us." I sometimes still do the stocking though... candy, hot chocolate, socks, body sprays, etc. Just small little things that I don't care about if it goes to waste. 

Gifts should be given jointly, in my opinion. You're married to their father and both of your income counts as marital income. I would let dad pay and you pick out the gifts. Most of the non-Santa gifts should come from both of you. Maybe dad picks out a gift for each kid just from him. A tiny trinket from you is thoughtful, but don't try too hard. Kids can smell an over eager Step mom from a million miles away. Don't set yourself up to be exploited in the future.

I used to do the gift buying (with both our marital money) and put so much thought into their gifts and DH put from both of our names. They are all lost, broken, unused now. 
I leave it up to DH now they are older. We have only gifted two presents each for them this year (one from Santa) and filling up their stockings with things like new socks and lollies. 
 

Since we married, all gifts for SS12 are from both DH and me and SS knows that. We have joint accounts, so no question of who pays. I'm a much better gift-giver than DH, so I come up with a lot of the ideas and he will do ordering. We shop together when we can, as we both enjoy it. Otherwise, he handles it.

In our case, we have no list. SS has never asked for anything. Why? Because BM buys him whatever he wants throughout the year. We now just think of things he might be able to use and no longer worry about getting him things he'll get excited about. Even when he was 6, he was pretty blasé.

We give a joint gift. Unless there is something that we individually want to give to someone.

For me, the first year or two I got a few small things from me personally to give to SD12, but as the last few years have went on it was apparent that she didn't really care about or respect the things I got her. This past weekend we (her dad and I) went up to her room with her and forced her to clean it out (filthy like always) and we were going through all her stuff with her and as we were pulling items out of drawers, under her bed, closet floor, etc. I pretty much came across everything I ever got her that was trashed, smashed, dirty, un-used and that's exactly the reason why I won't get her anything anymore and let her dad do all her gifts for every occasion.

Every family and child is different depending on how close you are but this is what I choose.

I have no good advice here as I am raising my stepchildren.. I treat them as my own. They get the same amount of gifts as my biological children, we also have them full time too so its just regular family routine here. If your married to the kids parent then I would just as a couple others have said here do joint gifts that way they don't know the difference unless you are all very distant or you are trying to enhance/strengthen your bond with them then I say go big or go home. lol 

Goodluck <3

I didn't read through everyone's comments but this is how I did it. 

When I did not live with them, I bought my own presents for them. Nothing crazy, a simple thing or two. 

When I moved in, it was a combined effort. All the gifts we bought (husband and myself) were from both of us! Our bills were together and such so it just made sense!

That's what we do.