The 3rd level spell Nondetection can be used to ward an item, or a creature and all the gear it is carrying, against divinations:
The warded creature or object becomes difficult to detect by divination spells such as clairaudience/clairvoyance, locate object, and detect spells. Nondetection also prevents location by such magic items as crystal balls. If a divination is attempted against the warded creature or item, the caster of the divination must succeed on a caster level check (1d20 + caster level) against a DC of 11 + the caster level of the spellcaster who cast nondetection. If you cast nondetection on yourself or on an item currently in your possession, the DC is 15 + your caster level.
If cast on a creature, nondetection wards the creature’s gear as well as the creature itself.
The list of spells mentioned in the spell description is not exclusive; the subject is warded against "divination spells" generally, such as the ones mentioned. Any Divination spell effect attempted against the warded target requires a caster level check to succeed, otherwise it detects/reveals nothing. The Detect Magic and Arcane Sight spells are both divinations and thus warded against by the spell.
The warding effect affects a character, their gear, and any active spell effects on them as a single package; anyone attempting a divination against character would make a single caster level check to overcome the single Nondetection spell, and if they succeed they'd be able to sense any of the relevant auras on the character or their equipment.
Nondetection must also extend to spell effects currently on the subject itself, because Nondetection is such a spell effect; it wouldn't really do an effective job of hiding you from magical detection if the effect itself was trivial to magically detect. Additionally, the wording of the detect spells states:
... If the items or creatures bearing the auras are in line of sight...
Which suggests that the aura of an active spell effect is quite tangibly tied to the character/item it targets, and the warding of Nondetection should apply.
Since it can be overcome by a caster level check it's not as reliable a ward against detection as Magic Aura is for items, but it does give you a good chance of evading such divinations. When used by a caster on themselves it's more effective, increasing the caster level check DC from 11 + Nondetection CL to 15+, which would give the sneaky caster roughly 30% odds of being detected by an enemy caster of similar level (and very good odds against items casting Detect spells, since they will typically have very low caster levels).
It's available in item form as the Amulet of Proof Against Detection and Location.
Another spell useful for evading detection based on your auras is Misdirection, a level 2 spell which disguises your aura by making you appear to be something else; however, it is overcome by a simple Will save by the detector, so does not scale in effectiveness with your caster level so much. But you can also use Misdirection to pretend to have the magical auras of something else, so it has a little more versatility of intent.
Mind Blank (not without anti-RAI lawyering)
The Mind Blank spell could be considered to protect you from such detection spells if you read it a certain way, owing to the highlighted portion:
The subject is protected from all devices and spells that detect, influence, or read emotions or thoughts. This spell protects against all mind-affecting spells and effects as well as information gathering by divination spells or effects. Mind blank even foils limited wish, miracle, and wish spells when they are used in such a way as to affect the subject’s mind or to gain information about it. In the case of scrying that scans an area the creature is in, such as arcane eye, the spell works but the creature simply isn’t detected. Scrying attempts that are targeted specifically at the subject do not work at all.
If you take that as a separate statement it suggests that no divinations will work against the subject of the spell. RAW, there's quite the argument to be had. The intention, however, is fairly clearly that the protections of Mind Blank apply only to effects which would read or affect your mind, and to remote scrying attempts. The closest I could find to official statements on that are reposts of posts from elderly forums:
Mind blank stops things that effect the mind, and scrying (divinations that work remotely without line of effect to the subject). Mind blank does not stop direct observation with a divination spell (unless of read the mind).
Q: You recently answered a question regarding the Mind Blank spell vs. the effects of True Strike, stating that Mind Blank does not affect True Strike. Many people resting on both sides of the issue we're hoping you could offer an explanation as to why it does not.
A: True strike doesn't reveal anything about a particular creature, so mind blank has no effect on the spell.
Q: In addition, there have been questions raised concerning how Mind Blank functions in conjunction with other spells. For example, lets say a wizard casts Mind Blank and Improved Invisibility on himself. Does the invisibility now count as part of the caster, or is it considered a separate entity in regards to spells like See Invisibility?
A: Mind blank is not effective against see invisibility (non detection is). Mind blank protects against devices and spells that detect, influence, or read emotions or thoughts. And against scrying, which is magical information gathering conducted remotely. See invisibility is not scrying.
Q: In other words, is the Mind Blanked/Invisible wizard protected from See Invisibility? Detect Magic? True Seeing?
A: No in all three cases.
Which, if you accept these sources as being true renditions of official statements gone past, explicitly denies that Mind Blank would protect you against Detect X spells.