The following characters are the ones you need to recruit in order of the story:
Alistar - Story recruit at Ostagar
Dog - Either comes with Human Noble or a mission while at Ostagar and Kocari Wilds.
Morrigan - Story recruit at Flemeth's Hut
Leliana - Recruited at Dane's Refuge within Lothering
Sten - Locked up at Lothering. Convince the Revered Mother to give you the key. With Leliana, you can also lockpick the cage.
Wynne - Recruited at the Circle. Make sure you do not have Morrigan in your party or else she won't join.
Oghren - Story join at Orzammar on the way to the Deep Roads to look for Branka.
Zevran - Recruited at a random encounter. Beat him to death and then let him live.
Loghain - Beat him in the Landsmeet duel and then spare his life. Forces Alistar to leave the group.