Through the entire series of Dr. Who, the doctor has usually had a companion with him. With the end of season 2 of New Who, you get a glimpse of a companionless 10th doctor who shows his dark side. Starting out in the beginning of season 2 you got a glimpse that this doctor was less forgiving and if push came to pull he wasn’t afraid to do what needed to be done. Then towards the end of The Runaway Bride you see a darker side of the doctor where he is just watching the emprise suffer and the only thing that snaps him out of it is Donna yelling at him. Then towards the end of the episode Donna tells the doctor that he needs to find someone (a companion) in which the doctor disagrees. She then tells him he does because sometimes he needs someone to stop him and then he agrees with her. This shows that even she sees that he can get out of control at times and that he may need reeling in.
The doctor is also visibly still upset about losing Rose, whenever her name is brought up he gets very quiet and sentimental. Him being by himself I believe is only making it tougher for him to accept that she is gone. We caught a glimpse of him with Martha and how he seemed much more like himself when they were together. This is what leads me to believe that the Doctor needs to have a companion with him so that he can move on from the previous one. Martha I believe will be a good companion for the Doctor because it shows that she is compassionate, which means she will help keep the Doctor in line and in check. With that in mind, I believe that the 10th Doctor should always have a companion not only to keep him in line but also for him to lean on.