[Update #1] Familiars' Handbook - Spellcasting Familiars Part I

This is a post that will be incorporated in the updated Familiars' Handbook.

So, the whole purpose of this post is to investigate the different ways that are available for a familiar to acquire the ability to cast actual spells, not through shortcuts, like feats that gain spell-like abilities or using charged or command activated, etc items - e.g. wands, scrolls, staffs, eternal wands. The most important benefit that a spellcaster gains if he decides to invest in a spellcasting familiar is that he is essentially casting extra spells, thus gaining a "Quicken" effect to his spells. It's true that a high-level spellcaster is going to use in-battle spells that are higher and keep his lower level slots for more utility; gaining a companion that's able to use both his high and low spell slots at the same time (with his familiar acting as a medium), is going to help a spellcaster to plan the order of the spells he is going to cast in a given battle more easily, both because you're actually using two characters with separate movement modes.

To sum up, sharing your spells with your familiar and enabling it to cast them gives you:
  1. Bonus Actions: A familiar has a full-round action or a standard action, move action. Plus you're got a swift action to use. Many spells have different casting times, so you can actually utilize more than your limited chassis is giving you. This feature is closely related with the Quicken Spell metamagic feat: you're using it to cast more spells per round than you normally can. 
  2. Extra Reach: Imagine that you want to hit an enemy with a range: touch spell, but you also want to heal your teammate with a touch spell. Under normal circumstances you'd have to use special effects that increase your range or just run from one target to the other in order to hit both; plus you'd have to spend two rounds doing so. Now, you can quite possibly do both, by having your familiar cast the second spell for you (to be clear - I mean that the familiar casts the spell itself, not that you're using the deliver touch spell special feature). At low levels, where things like range matter a little bit more (you might not have enough!), the extra few feet that you or your familiar can move and cast can also be of importance. Relating this bonus to metamagic feats, it's like having an Enlarge Spell or Reach Spell metamagic effect. 
  3. Extra Duration: This is closely related to the "Bonus Actions" entry. I hate it when I spend actions buffing, even though I know that buffs are an important aspect of the game; this is why people like to have daily or long duration buffs, so that they will be always ready to face their enemies in an optimal way. However that's not always the case - certain buffs might not be applicable for Persistent Spell or you might not have access to it altogether; or you might need a more case-specific spell that's not worthy of being persisted. Whatever the case, having a familiar that has access to utility buff spells is going to provide a free buff round for you or a teammate; the only way to get a free buff round before an encounter is if e.g. buff yourself before entering a room, but you don't actually know if the room will contain an enemy or not, or  environmental variables might hinder you in such a way that you'll lose precious buff duration. This bonus is more or less like the Extend Spell feat being applied to your spells. 
  4. Flexibility: This is applicable to situations that you'll need ad hoc buffs - i.e. those buffs that are not universally good, but only against certain enemies. This point is again closely related to the bonus actions entry, but I decided that it's good enough to warrant separate elaboration. Again, in the situation that you'll try to buff yourself before entering a room to avoid losing actions in the first battle round, you're investing in duration, but, also, unless you have investigated your target enough, you're also losing on spell options; this means that a wizard that doesn't have enough information about what's on the other part of the door, will most likely cast a universally good buff instead of an ad hoc buff (e.g. a spell that protects only against the undead), because the risk factor is actually higher than the returns you're getting - in the first case you'll get some bonuses, but in the second case you might get nothing. 
That's pretty much the basic chassis of benefits you're getting by investing in a spellcasting familiar. You're quite possibly giving up some feats (if you don't have access to a Summon Familiar class feature) and/or spell slots and/or resources, to effectively gain more actions per round, some amount of reach depending on the situation, a bit more flexibility and some duration. 

To actually gain the benefits above, however, your familiar will have to be able to cast spells in the first place. In order to accomplish that we'll have to use one of the following methods:

Spell-Linked Familiar

This is probably the most straightforward method that you can use to give your familiar spells; the feat appears in the sourcebook Player's Handbook II and it has some really interesting requirements: it requires you to have an arcane caster level of 9 in order to get it and it gives scaling benefits depending on your arcane caster level. There are some abilities that boost your arcane caster level, for instance the Ultimate Magus prestige class, from the sourcebook Complete Mage, but, unfortunately, they are quite scarce. What this means is that unless you're going to use special techniques, you'll be able to acquire this feat at level nine.

The biggest downside of Spell-Linked Familiar is that it doesn't scale as good: your familiar can cast at most second level spells, which is not necessary a bad thing, but at level 15 (the sooner that you'll get second level spells from your familiar without increasing your caster level with other methods), it probably means that the spells will be utility buffs rather than offensive. Note that actually, while the feat requires you to have an arcane caster level, you are not limited to transferring arcane spell slots to your familiar; you can transfer divine spell slots as well, as in the feat's text there is no special distinction to spell slots between arcane and divine. Your spell selection to be passed to your familiar is limited even further by the fact that when casting, your familiar uses only one half your caster level, so spells that have spell resistance or spells that depend a lot on caster level for duration or damage are probably out; additionally it can't cast spells that have an XP or a focus component, which, excludes some worthwhile spells, but it's not that limiting. Fortunately, there is a minor benefit to the feat - your familiar doesn't need somatic, verbal or material components in order to cast the spells that you're giving it; obviously the important part isn't the fact that it casts all spells Stilled and Silent, but the fact that there's an Eschew Materials thing going on, which has weird interactions with some spells: for instance, take Launch Bolt from Spell Compendium - arguably you can use Eschew Materials (and by extension Spell-Linked Familiar) and Launch Bolt together in order to create and shoot gargantuan bolts at your targets, doing 4d6 with a ranged attack roll, which is ok if it comes from your familiar by using a 0-level spell. Do note that Spell-Linked Familiar doesn't have a maximum of 1gp material component value, as Eschew Materials - items that have a gp cost are excluded; whether spells that have a cost in silver pieces are affected or not (I'd say they should be, as silver pieces can be translated to gold pieces with a simple division).

Something that's not clarified in the feat's entry is what attributes the familiar uses in order to cast the granted spells; if it uses its own stats then in most of the cases (unless you're high enough level to give it extra intelligence) it might not even be able to cast arcane spells altogether. If it uses your own stats, then save-or-die (or suck) effects might be effective, if they don't depend on caster level (e.g. if they allow spell resistance).

So what spells should you transfer to your familiar? You can use it to get the maximum duration from spells of the Detect X line or other low-level duration:concentration spells, so that you always have all of your actions available (unfortunately, a great first level spell, Silent Image, is excluded, because it requires a focus). In the case of familiars that have superior camouflage abilities (e.g. high hide and move silently scores, small frames or even Imp's invisibility) you can provide it with spells that increase his espionage power - an example would be giving it a Comprehend Languages spells, so that it won't have a problem when dealing with languages or speech that it doesn't understand; others can be, e.g. Disguise Self or Floating Disk. However, the majority of the spells will be items such as Protection from X, Grease, Enlarge Person, Reduce Person, Feather Fall, Obscuring Mist.

This method is for: characters that do not want to invest much of their resources to a spellcasting familiar; characters that are not feat starved; characters that do not need to reserve their high feat slots for key feats.