Southwest: SWA is cool with you checking two bags for free (max 50lbs each), but beyond two will cost ya. This generous allowance is actually one huge reason why families love Southwest.
JetBlue: Although there have been some whispers that JetBlue may begin charging in 2015, for right now the airline sticks by its first bag free policy (up to 50lbs). Naturally, carry-on luggage is also complimentary, so long as you don't go overboard with the allowance.
If you're traveling often enough with checked bag to be bit in the butt by fees, consider making a dash for elite status. Airlines often offer free first or even second bags complimentary to frequent flyers of their loyalty programs. Of course you'll have to pay to get the required number of flights, miles, or spend, but you could be close to the goal without even knowing.
*Note that these refer to domestic flights in the United States. Most airlines offer at least one free checked bag on international routes, although you should always check with your carrier for the latest updates.