I really want to post in this even though probably everyone's forgotten about it...
Maul was 100% loyal to Darth Sidious. He never thought about betraying him (even Sidious knows this), which isn't exactly ideal in a Sith - when the apprentice is strong enough, he/she can overcome the master and become the next Sith Master.
Also, Maul was a pawn for Sidious. Which means that he was useful to a certain extent. And it would have taken an even longer time for Sidious' plans to unfold. Why? Because Dooku had all the connections - he was a political leader, and was very wealthy. Maul had none of that. Sidious needed Dooku to launch the Clone Wars and build armies. Maul was simply a warrior.
Therefore, as cool as Darth Maul is, I think his death in TPM was necessary as far as story goes. He's a cool evil dude, but he doesn't do much more than that. Heck, he only speaks once in the entire movie!
I'd agree with others that Maul would have made a crummy head Sith. However, having Maul around a lot longer probably would have suited Sidious just fine. The Sith Rule of Two is intended to keep them from in-fighting, and yes, when an apprentice becomes more powerful than the master, he knocks him off and becomes the new master. But having an apprentice who craves the top spot is only important if the master will eventually grow old and weak. Palpy seemed to find a way to prolong his life, possibly indefinitely. Given the circumstances, an extremely powerful, but loyal apprentice who wouldn't betray him was probably the best possible Sith apprentice, and maybe even more preferable than Vader. His death forced Palpy to recruit others, but I think its totally plausable that Sidious initially intended to wipe out the Jedi with Maul by his side.
I saw the battle with Obi and Maul very differently as well. Obi-Wan didn't win that fight because he was a better fighter or stronger in the force. Maul was overconfident and wasted time taunting Obi when he should have just finished him off. Obi's perseverence allows him to take advantage of all this when the time is right.
Dooku definitely seemed like more of a stop-gap than an intended long term apprentice. I'm again drawn to Sidious's intentions though...why would he want Dooku to stick around once the Jedi were gone when Dooku was easily ambitious enough to try to off his master? Much better to use him as the face of the Sith, then off him at the end of the war.
I'm probably in the minority, but I liked the Visionaries story with Maul getting artificial legs and tracking Obi-Wan to Tatooine to get revenge. I would have liked to see him get more screen time and wish they had done much more with him (let's be honest here - he's really the only thing good about E1).