First off, I would like to see animal companions and familiars as class options rather than as default class features. Either give wizards, sorcerers, psions, druids, rangers and paladins a bonus feat with which they can acquire a companion or give them a set of optional class abilities one of which is a companion of some sort. Not every character concept includes a sidekick creature, so a player shouldn't be made to feel like they're loosing out for not taking one.
Next, for familiars, I'd arrange for them to have some clear magic-related benefit for arcane casters to want them around. Traditionally, in folklore, familiars serve spell-casters as remote eyes and ears but also endow their masters with some mystical aid to their spell-casting, either by teaching them their spells, guiding their progress or by lending some extra magical power to help control their magic. I'd like to see that reflected in the rules somehow. Perhaps familiars could grant extra spell points (or their equivalent), grant bonuses to spell penetration rolls, grant bonuses to savings throws against magical affects, increase the save DC of their master's spells or grant the ability to forgo a component from each cast spell (either somatic, vocal or material) whenever the familiar and master are in physical contact. Perhaps it'd be easiest to have the familiar grant the benefits of a metamagic feat to their master. Perhaps all of these ideas could be balanced against each other and the player could choose amongst the lot when they acquire a familiar. Other such abilities could be gained as the PC advances in level.
Lastly, as others have suggested, I'd like to see more exotic options for familiars right out of the gate, including small balanced elementals, undead, fey, constructs, aberrations and even sentient items (crystals, staves, books, etc.).