Generally off-topic. Suggestions for games that meet specific requirements. (tag exists primarily for historical reasons)
Why no more recommendation questions? There was extended discussion on the Board and Card Games Meta site regarding whether or not to support/tolerate/allow recommendation questions. This culminated in a comprehensive ban. You can read the final decision and discussion thereof here, and searching the meta site for "recommendation" while let you catch up on the history.
Some recommendation questions can be shaped into good, allowable questions. In the comments on the meta discussion linked above, someone asked about the question "What games can I play with my blind son and my seeing son?" As is, this is a recommendation question that we'd rather not have. One of the issues about answers to recommendation questions is that voting is more of a popularity contest than a measure of quality, which would be an issue here. However, reworked as "How can I play games with both my seeing children and blind son?" it becomes a question where more ideas could be shared, often with specific examples to back them up. There's a strong possibility of more helpful, creative answers that could be voted on somewhat objectively. That said, if you're just interested in finding more deck-building games like Dominion, try some of the resources below.
Where should I go for game recommendations?
The Board and Card Games Chat is a great place to ask for recommendations, or to just shoot the breeze with other board gamers. Don't be discouraged if no one's there, just leave a message and people will tag you in responses so you get notified.
Boardgame Geek has lists and reviews, lets you search games by categories such as number of players, game mechanic, and appropriate age, and forums where you can ask for all the opinions you want. Most online retailers selling games have reviews and can help you find games similar to others that you like.
Your Friendly Local Game Store: Do a search, you might be surprised at how many there are. Other customers and the staff are great people to talk to about what you like, and they can usually help you find something and even let you try it out before buying.