I don't think there is an easy solution to this.
I do think that you should design the game engine acording to targeted audience. So you should optimize your game engine acording to the most comon aspect ratio used on your targeted platforms.
I don't think making different UI's for different aspect ratios is a solution. For instance if you make a bigger UI for users with widescreens you won't achive the same gameplay expirience with those who use standard monitors and would have smaler UI. Especialy if widescreen UI contains more information. So becouse using differen UI won't offer the same gaming expirience showing more world would be much easier solution to do.
But if you do intend for all of your players to have the same gaming expirience then you should lock your games aspect ratio so that only resolutions of that aspect ratio are posible. Also in this case you should take care so that all ingame object are drawn the same size regardles of the screen resolution.

Now as for using different resolutions (DPI's) you should use several instances of your graphics optimized for several different resolutions. Using only graphics optimized for high resolutions and scaling them donwn will make them look blured an lose some importand detailes. (slowly scale down any of your photos in your popular photo editing tool and you wil quickly inderstand what I mean). Also using grapphics optimized for small resolutions and caling them up will make them look pixelated (each pixel will look like smal square).
Offcourse you don't have to make graphics optimized for every posible resolution, you should make your graphics optimized for most oftem used resolutions and then scale them for other always using the one wich are the closest to the target resolution (les scaling means better results).

The best way is to use vectored graphics but as it has been sad not all of the graphics can be vectorised. So this means that the grephics must be developed acordingly from the verry start.

@Little offtopic
Widescreens could be easily used for making games with hotseat multiplayer by splitscreen method (verticaly spliting the scren into wto parts).