Capital One will only issue one card per person in a six-month period. But within those confines, they do place a lot of weight on how you've done with their previous products. If you happen to apply too soon, they'll simply tell you that you're "not eligible" rather than pulling your credit. Be aware that the one thing they're sensitive to is too many recently opened accounts.
With Chase, you absolutely don't want to apply for two cards at once. What happens is that they'll happily approve both applications, then they'll figure out what they did and shut one of the cards down a few days later. Yuck. Some say that 30 days between applications is OK, but three months would be a whole lot safer. Keep in mind that Chase is also sensitive to recently opened accounts. If you plan to apply for a second Chase card in three months, don't open accounts with any other bank during that timeframe.
With some banks, you can definitely open two cards on the same day. I'm not confident listing any examples off the top of my head, but I'm sure someone will chime in with that information. 
@HeavenOhio wrote:
With some banks, you can definitely open two cards on the same day. I'm not confident listing any examples off the top of my head, but I'm sure someone will chime in with that information.
AMEX. Its not rare to have someone open up a revolver and a charge card the same day. Occasionally someone manages to get 2 revolvers the same day but that's atypical.
Prequals are your best bet.
Check Cap One, Discover, BT&T every month.
GL!
@Anonymous wrote: I see alot of sigs that show multiple cards from the same lender. I'm curious how one goes about building that ...This is more for future knowledge than anything else.
As one member with multiple cards from the same lender, the basic answer is (1) Time (and lots of it) and (2) Patience. Treat any lender you want more cards from as a relationship and groom it. Use the first card you have regularly and responsibly. With some lenders, having banking accounts, investments, or loans that you manage responsibly will also help. They may even send you preapproved offers for more cards! Don't rush the process or seem desperate. Allow each to grow and blossom as it will. Remember that building credit is a marathon, not a sprint. Enjoy the journey!
Multiple cards with one lender is fine, but remember to build diversity in your lineup. I target a variety of big national banks as well as great credit unions to spread my exposure. If one lender were to take adverse action, they can only have a limited impact on your total credit limits, utilization, and scores. Plus many lenders are much more comfortable with seeing your credit risk is diversified.
*I currently have multiple cards with Chase and Bank of America, the two largest banks in the US. Larger lenders seem more in favor of issuing multiple cards. (My longer term plan is to consolidate some of those Chase credit lines.) Previously I've had multiple cards from other lenders also. Some smaller financial institutions may limit you to only one, two or three cards, or they may only have that many total brands of cards! 
