[zylosan]

Several types of spirits have the Magician quality and can cast spells. Can those spirits be initiatied.  I know spirits can just know metamagic but can they benefit from the increased magic aspect of initiation?

[Lethe]

I assume, you are talking about free spirits. Then all of them have the magician quality.

It also acts as the spirit’s Magic attribute. Force increases can be purchased at character generation for the same price as any attribute. The natural maximum for the Force attribute is 6, although this can be later increased through initiation. [...] A free spirit may join a magical group. [...] All free spirits have the Magician quality at no cost.

[Orvich]

Yes, you can have a free spirit that has initiated. They spend karma on it as normal, but receive a new spirit power instead of a metamagic.

No, you cannot have a normal spirit that has initiated. Their Magic attribute is always set at their Force.

Page 107 of Street Magic, for how Free Spirits spend Karma.

EDIT: And no, spirits cannot have metamagic. They sometimes have Spirit Powers that mimic metamagics, though.

[Lethe]

Yes, you can have a free spirit that has initiated. They spend karma on it as normal, but receive a new spirit power instead of a metamagic.
EDIT: And no, spirits cannot have metamagic. They sometimes have Spirit Powers that mimic metamagics, though.

The book seems to disagree with you.

Additionally, for each grade of initiation, the spirit may either learn a new metamagic technique (but not Invoking or Sensing) or gain one Power Point.

[Orvich]

These rules cover the play of free spirits as player characters. A PC free spirit is somewhat different than an NPC. The PC has a greater level of detail, because, as one of the story’s protagonists, it is more important than NPC free spirits. As such, they follow somewhat different rules. Unless otherwise specified, all references to free spirits in this section denote PC free spirits (NPC free spirits use the rules on p. 106, Street Magic, unless the gamemaster  chooses otherwise).

Nah, I think I'm good. By default it goes to Street Magic rules, which are as I described above, and quoted below, from StM: 107

A free spirit can use Karma in several ways at normal character costs (see Character Improvement, p. 263, SR4). Spirits normally have no racial maximums on their skills or attributes.
• It may raise its attributes separately (which all begin at the Force it had when it went free).
• It may raise or purchase additional skills.
• It may initiate as a magician does, though the process grants one  additional  free  spirit  power  per  grade  rather  than  a metamagic technique.
• It may raise its Force by 1 point at a time at the cost of new Force rating x 10. Raising Force raises all of the spirit’s attributes and powers that are based on Force.

Because the OP seems to be talking about spirits in general, and this isn't the character creation subforum, these rules are probably those that he's looking for.

[Lethe]

Sure, your quotes are good, but since the Runners Companion is the more recent book, its rules are more refined and show whats possible. The only example free ghosts Buttercup and Gwynplaine both have metamagics as well.

[Orvich]

I agree, Runners Companion is the newer book, and is therefore default for rules! And Runners Companion names the Street Runner rules as the primary rules for NPC Free Spirits, as seen in my quotes. If he's looking for NPC spirit rules (which again, I think is likely), it's Street Magic he wants - according to Runners Companion!

As for the sample characters... I'd like to note both that they are sample characters and therefore probably not NPC freespirits, and according to reviews of the book in which they appear, they disregard normal rules anyways! Quoting Umaro from that thread:

I'm assuming that the various ways Buttercup works completely differently from other free spirits (like being able to Summon, or apparently being able to earn karma without making spirit pacts) is because she's too cool for rules.

I don't have that supplement, but I think I know someone who does and I'll page through it. But this argument is stupid. I quoted the relevant parts of the text, verbatim, and the text is very clear on this point. Let's not confuse things more. If you don't like the RAW, houserule it, those houserule things are darn cool.

[Lethe]

NPC free spirits use the rules on p. 106, Street Magic, unless the gamemaster chooses otherwise

If you mean this rule, its not really houseruling, if the book gives you both option anyway.

The PC has a greater level of detail, because, as one of the story’s protagonists, it is more important than NPC free spirits.

If you want to flesh out your NPC free spirit more, i.e. for a repeating antagonist, i very much suggest to take the rules in Runners Companion.

And since the the OP is already asking about metamagic and initiation for free spirits, i am pretty sure, that is what he is looking for.

[Demerzel]

Ran across this today, and it made me think of this thread.

Street magic page 107, third bullet, "Any of the metamagic techniques available to metahuman initiates may be taken as a free spirit power."