In Dungeons and Dragons and perhaps a few other games as well, characters are assigned an alignment depending on their position regarding good, evil, or neutrality between the two as well as their behavior and views in respect to law, chaos, or neutrality. The alignment standards usually do not take into account shades of gray and another fact is alignment does not necessarily dictate character personality (an evil character may have some emotional ties whereas a good character would be completely cold and distant, etc.)
In Death Note the characters have shown tendencies towards having certain alignments, though alignments in DN characters usually shift, change, or character alignments might be ambiguous depending on how and when they are looked at.
I am going to open the Pandora's Box of debate here and give my interpretations on character alignments, though if a character has multiple debatable alignments I will assign accordingly. I am throwing these out there for discussion purposes, this is of course not the be all and end all of character morality and personality.
Needless to say, this will also contain spoilers.
Light Yagami: Lawful Evil
Light starts out in the beginning as Lawful Good with a desire to rid the world of evil and see justice for the innocent, carrying this out with the power of the Death Note. This absolute power, of course, corrupts absolutely. Light gradually becomes power hungry with a desire for dominance and is not shy about killing off anyone in his way, even family members. Manipulating laws to his own advantage and the desire to dominate (become the god of his own world) is characteristic of Lawful Evil.
L: Lawful Neutral...
L from the offset is motivated by a sense of justice to see criminals such a Kira brought down. He himself is willing to break laws and occasionally see people come to harm for the sake of his investigations. He is also a bit selfish, though not as ruthless as Light is about getting what he wants, meaning he's not good though he doesn't display obvious evil...obvious anyway which brings us to the other alternative...
...or Lawful Evil
L isn't as power hungry or ruthless as Light is, though some of his views and actions could make a case for him being on the lighter end of the Lawful Evil side. He already possesses great amounts of power in the ability to control any agency from police to world leaders which is already a fuzzy moral place to be. He thinks nothing about collateral damage or torturing people to get information. As for his sense of justice, it is pretty much said in Chapter 109 (the extra chapter) that he doesn't operate on a sense of justice and considers solving cases to be a game.
Misa: Chaotic Neutral, or Neutral Evil
Misa is very fuzzy alignment wise. has no qualms about killing people with the Death Note, though she doesn't seem to do this out of malice and essentially does it to gain Kira's attention. On one hand she is willing to do anything to get what she wants and is calculating, making her a bit NE, though she also seems to have a sense of detatchment from the killings and is motivated more by love for Light and loyalty to her parents' memories. This could indicate she is neautral and doing this for her own kicks and not out of a sense of evil or is motivated enough by her jealousy, anger, and selfishness to be truly evil.
Ryuk: Chaotic Neutral
I think Ryuk is a classic case of CN, motivated by his own desire to shake things up than for any good or evil purpose. He is definitely a free spirit with who wants to go his own way, reveling in the chaos though not having a sense of malice.
Soichiro Yagami: Lawful Good
One of the only characters in this series truly motivated by a sense of right and goodness. Soichiro follows the laws, though upholds his own sense of right even when the laws fail (such as when the NPA bows to Yotsuba). He is motivated by his sense of right as well as his love for his family and loyalty to his fellow police officers.
Near: Lawful Neutral
Near, like L, is motivated by putting away a killer though his situation is made personal by the death of his mentor and the eventual death of his peer. Near appears to be a lot more neutrally inclined than L. He does tell a few lies and manipulates circumstances to get his own way, though seems a lot more neutral and collected in his approach to situations. Near is at best a thinker and at worst a machine.
Mello: debateably Chaotic Neutral to Chaotic Evil
Mello in the beginning displays the hot-tempered and violent nature of someone who is Chaotic Evil and has a do it at all costs attitude of someehat of this alignment as well. His actions are, however, debatable. He said he didn't mean for Soichiro to die and was clearly shaken by Matt's death. The kidnapping of Sayu Yagami and Kiyomi Takada and the deaths of the soldiers who raided his hide-out the first time also fall on the evil side though they could have been done out of calculation and necessity than pure malice.
Teru Mikami: Lawful Neutral to Lawful Evil
Mikami is also motivated by his own sense of justice against criminals, though his actions and motivations become twisted as the story goes on. He seems to take a little too much glee out of killing criminals (choose your poison: SAKUJO! or DELETE!) and he serves Kira loyally, though seems more content to be a servant than a budding leader giving him less of the ambition of an LE individual though the motivation is still there.
Kiyomi Takada: True Neutral
Kiyomi has a sense of loyalty to Kira's cause, though she doesn't display any real malice or altruism. She is motivated by her career and her ideals and that is pretty much it.
and for kicks
Beyond Birthday: Neutral Evil
B clearly enjoys killing people and makes a game out of causing people harm, whether obvious physical harm to his victims or emotional harm to his idol/rival L. B, however, is not random or chaotic in how he does things. He meticulously chooses his victims and sets up the web of his killing spree to every last detail. He may be malicious and unbalanced, though he knows what he is doing and is capable of acting civil in Naomi's presence.
These are pretty much the baseline characters. There are a lot I haven't included so feel free to discuss any other characters I may have missed. Like I said this is for discussion and is not a be all and end all of character personalities and there is probably a lot of things I missed here.