What are the most popular crypto currencies after Bitcoin? I am trying to determine which crypto currencies are the most popular with the assumption that Bitcoin is the most popular one.

This question is up to different interpretations because "most popular" can be viewed many different ways and that is why I am here asking this question.  Most popular could be based on the most real world use, the most media interest, the most valuable, or the most number of people mining or the most processing power used in mining.

I want to know your opinion based on solid facts of the current state of crypto currencies.  It could be that another crypto currency is more popular than Bitcoin based on your rank, and I doubt that, but that is why I want the help from experts here.
If an online store accepts another crypto-currency appart from Bitcoin, you can be sure 90% of the time it'll be Litecoin (most accept just Bitcoin as of now). It's the one that has the 2nd biggest market capitalization and market depth as well. As to what could be the 3rd most popular, that's difficult.

"Popularity" is difficult to measure directly, but you can use value in fiat as a proxy. Right now, several crypto-coins are valuable about 1 US dollar or more: just go to cryptsy or to coinwarzand check the market prices (given in bitcoins). Given current prices of bitcoin in USD anything more valuable than one milli-bitcoin is worth aprox. a dollar, a lot of coins are worth more.

Another proxy you can take is how frequently you see ads of people asking for donations or offering their services in exchange of that currency - that way, you'll see humble dogecoin being asked/offered a lot, where as protoshares/quarks are almost never asked for in spite of their value. Other coins worth more than a dollar (like prime, name or PPC) would take the lead here based on this metric.