We have used a few with good success -
Nitrosell - highly automated, lots of built-in features, 50K Item limit, GUI, Web Catalog builder/Item management;
24x7 Cart (Lan Services) - lots of options, tight integration, GUI, Web Catalog builder/Item management;
bLoyal - emphasis on Loyalty, Clubs, Order processing; GUI, Web Catalog builder/Item management
nChannel - Magento and Accounting integration, GUI, extension options;
And maybe a couple of others. These all have various options for Mobile stores, eBay/Amazon etc. links, etc.
Some use only their own cart and process; others have links to mainly one site but are willing to look at custom work. They are mostly in the same price range, nChannel more because the same platform and GUI can be used to integrate Accounting/ERP systems, and the Website is separate.
Nitrosell Ecommerce and bLoyal Loyalty also work together; I had bugged them for years to get together, guess maybe others did too.
I have spoken to i95Dev and their sites look very good, and their integration looks OK (no GUI or Web Catalog builder, just runs in the background) but we haven't worked with them yet. Also has Accounting/ERP links. Similar pricing to nChannel.
We and other users I have spoken to have had issues with a couple of others I haven't mentioned here, including some that have been around for a while - not sure if this is the place for reviews and such, but if they are not mentioned here you may be forewarned.
I also looked at Channelbrain, but that was recently purchased by one of those others. I reached out to them by phone and email to see if they had improved - but it's been at least a couple of weeks and no one has replied - so par for the course it seems.