---This is quite a long review, but this is based on my many years of experience of having played the game since it came out on the Dreamcast---
Ikaruga is the 'spiritual successor' to the once darling of ebay, Radiant Silvergun (this was because that game was only available on the Sega Saturn and as such would often fetch a high price).
As is typical of Treasure, the game excels in a few key areas: style (which includes technical and graphical prowess), gameplay and boss fights.
Stylistically Ikaruga still looks amazing even by today's standards, and features some of the most beautiful artwork of any game I've ever come across - just take a peek at the cards for an indication of what I mean.
The style is married to what seems like a very simple gameplay idea that focuses on two different polarities: black and white - something they explored in one of their earlier games called Silhouette Mirage. During the game the player will encounter enemies of either one of these polarities, and will soon notice that they may inflict more damage upon enemies if they are of the opposite polarity. Likewise if players are shot by a projectile of the opposite polarity they will die.
As you can imagine things get a little tougher as you progress through the game, however it's here that the many intricacies of Ikaruga's combination of style and gameplay become apparent. For instance one should bear in mind that it can actually become more difficult to play on Easy difficulty than it is to play on Normal, for on Easy the enemies do not fire any bullets for the player to absorb. Absorbtion of bullets not only add more points to the player's total, but also allows for a super attack that can clear a set number of enemies (depending on the level of the superbar prior to its unleashing and on the polarity of the player and enemies).
Leading on from this one of the most important parts of the game is its 'chain' system which might sound simple enough, but which offers a great deal of challenge from the offset should the player choose. This core aspect centers on shooting down three enemies of the same polarity to create a chain, which adds a multiplier depending on how long the player can keep it up. This invariably leads to players frantically switching during the course of play in order to accumulate points, to not get hit and to maintain that all important multiplier.
With experience the player can calculate the exact number of enemies that may be dispatched with their super move depending on the level of their superbar, and this is important so that players who are striving for higher points do not accidentally destroy more enemies with the super move than they intend to - thereby possibly ruining the chain multiplier. It gets a lot more intricate than that, but this is where the amazing fun and challenge derives.
A typical Treasure trait is to also incorporate epic boss fights and while it may not be on the same awe-inspiring level as those found in Radiant Silvergun, they do offer a worthy and interesting challenge. As an intersting sidenote, Blizzard later incoporated Ikaruga's polarity mechanic in their Twin Val'kyr boss encounter (which was part of the Trial of The Crusader raid instance), and I feel this is testament to the type of challenges that can be offered by a relatively simple gameplay mechanic.
In conclusion then Ikaruga is a truly amazing game because it introduces a relatively simple idea for any player to easily pick up, but which at the same time offers many intricacies and challenges for those willing to delve a little further.