Spellcasting is by far the most common use of Belldandy's powers. These spells are invoked by incantations which sound like formal prose. The words themselves dictate the meaning of the spell, whether it be used to create rain, make people sing together or assemble a circuit board. Unlike Urd, Belldandy's spells are quite precise and accomplish only the tasks they were invoked for.

Occasionally, Belldandy casts spells in Yggdrasil code speech. These are presumably the more complex spells since code speech compresses very long instructions into fewer (and harsher) sounds. An example is a spirit imprint (left lower image) which is used to play back a series of events that occured near to some object.

Belldandy only does divinations rarely. In Chapter 51 (You're So Bad), she uses a crystal ball to confirm her suspicion that Skuld has been growing in power. In Chapter 89, she does a runic divination for Urd to predict an upheaval and reconciliation (referring to Urd's reunion with her "long lost" angel, World of Elegance). In the same chapter, Urd mentions that Belldandy's divinations are good or accurate.

Only Bell has shown any affinity to animals in the series. In fact she can talk to them directly, like in Chapter 44 (Queen of Vengeance) where she was looking for a lost sweater. Bell also asked the birds in Chapter 67 (Fourth Goddess arc) to look for Keiichi.

Offhand, intelligence does not seem to be exactly a power. However this aspect appears to be more than sheer brainpower in the case of the goddesses. For example in Chapter 4 (College Exchange Goddess), Bell sits in a university classroom for the first time and later goes to solve something regarding energy output coefficients. Later in Chapter 8 (The Megumi Problem), Megumi tries to stump Bell with a variety of hard questions, all of which she answers flawlessly. I find it hard to believe that Bell was taught radio frequency electronics, physics, higher math, and even Japanese in Heaven. The more logical assumption is that Bell uses her link to access Yggdrasil's database. The fact that Urd loses her skill to ride a motorbike in Chapter 34 after losing her goddess license lends futher support to this assumption.

Expanded Senses / Clairvoyance

Apparently goddesses have much more acute senses than mortals. In Chapter 22 (Winner Takes All), Belldandy was able to master driving a go-cart by reading the actions of the top driver and emulating them to such a high degree of precision. In the continuation of that chapter, she uses all her senses to become a sort of real-time navigation computer in a rally race. Note that these were achieved by a combination of powerful senses and computational ability. While Belldandy might be capable of the latter on her own, it is entirely possible that she uses her link with Yggdrasil, as mentioned above. She could upload the raw data, let Yggdrasil crunch it and then download the processed data.

Voice Control

By mixing a spell with her voice, Bell can exert influence on the listener's will. She uses this on the arrogant Etsushi Ohtaki (Chapter 12, Leader of the Pack) to make him leave. (Note: If you're familiar with the famous sci-fi series Dune by Frank Herbert, there's a similar technique called the Voice although it doesn't use magic.)

Healing

Belldandy uses healing only rarely, and then in various forms. In Chapter 3, Belldandy kisses Keiichi's wound and heals it by accelerating metabolism. Four chapters later, she mistakenly thinks Keiichi has a cold and uses a complex spell to soothe him. Bell also heals by simply placing a finger over the injured area and channeling some energy.

Since the physical bodies of the goddesses are created by manipulation of atomic structure, they can also readily change their size and even split. Belldandy minaturizaed herself to conserve power in Chapter 41, and in other chapters simply to be less obvious. If I'm not mistaken, Belldandy only splits once (in Chapter 30, Mystical engine) unlike Urd who uses this technique often.

Air elemental magic is a late addition Belldandy's repertoire of powers. This part of her magic was defined only after the debut of Holy Bell since all the present angels (except those of Rind) have elemental domains (air, water, fire and earth). Belldandy uses wind-based powers in later chapters for various purposes, such as knocking people out (Holy Wind Press, Chapter 81) or cutting out the air supply of an engine to stop it (Air Bug Spiralee, Chapter 120). Bell often uses Holy Bell in casting such spells. In several cases Holy Bell intervenes directly, such as in Chapter 126 where she creates a cushion of air to save Keiichi (top image).

Air elemental magic is incompatible with Water elemental magic (Skuld's domain), the latter requiring Fire magic (Urd's domain) to counteract it.

As Urd explains in Chapter 131, goddesses can cast spells in the form of songs, these being reduced magical commands. As such, these songs are sung very precisely because they won't work with even one note off. Bell uses songs in several instances in the manga (e.g. Chapter 79, 131, 137) as well as in the Movie. Skuld claims that Belldandy's song is number one in Heaven.

The spiral bug driller, as the name implies is a device used for drilling through earth. Although it seems like an invention Skuld would make, this was actually created by Belldandy by casting a spell. Bell used this to create a hot spring.

The earrings of Belldandy have little trinkets than seem to be purely ornamental but actually contain various devices. These are used only in the early part of the manga.

Paralysis Field

This device generates a field that paralyzes an opponent without hurting them, much like a containment field. Bell uses this against a third class earth spirit in Chapter 9 (Apartment Hunting Blues) to prevent him from possessing Keiichi.

The manga describes this stone as: "The Maxwell's Demon has the ability to separate fast from slow molecules. He lets fast molecules into his room but slams the door on slower molecules. Consequently, as the room fills up with fast molecules, it quickly heats up. The demon pushes the hot gas out, then fills the room up again, over and over." In practice, the stone can be used as a propulsion system. Belldandy attaches this stone to a broom in Chapter 21 to make it fly. Urd also loans her stone to Skuld in Chapter 44 so she can make a rocket to put a satellite in orbit.

Transmitter

One of the trinkets in Bell's earring is a transmitter. She used it to track Urd in Chapter 25 (Love Potion #9) who had gone chasing after many men while under the influence of a love potion.