My list/checklist needs are fairly simple - the one I use most often is a "going out of town" list - not so much a packing list as a chores list - things I have to do before leaving so the house and cats are secure and survive until I return.
For this simple list I have just been using the note ap in my iphone and ipad. Syncs well between the two.
For more detailed checklists - I create them in evernote or word or excel - and have them as PDF's. I put these checklists in my dropbox (easiest way to get the file on my ipad) and then anotate the PDF (use it as a background) in Note Taker HD - the advantage to me of marking up the pdf is that in addition to physically checking an item off - if I make other notes or add things on the fly I have a record of those changes that I can add to the master document when I return to my office.