I really enjoyed Bungie's past user interface design in the Halo games that they developed, in my opinion, I think Bungie has had some of the best menus, game lobbies and HUD's out of the all the games that I have played. I hope Destiny is no exception, but it is hard to get that perfect mix of functionality and pleasing aesthetics.
Look at Halo 4 for example, I find the lobbies and menus are pretty nice looking, but they don't offer easy maneuverability. Then with the in game HUD, I find it's way too crowded for my liking; I can't stand the way they have a bunch of arrows pointing to guns on the map and grenade warnings, etc.
From what we've seen so far, I really like the HUD in Destiny. My only suggestion would be maybe some changes to the players or enemy name-tags. Right now it seems like each players numbered rank is what you will first notice when looking at your comrades.
I'd like to use the name tags as a way to really differentiate team mates by including each players customization. I'd really like to see player emblems and own custom colours above their heads, much like Halo 2 multiplayer. Also the return of full Gamertags not being displayed until you look in the general direction of the player could be nice to have less letters cluttering your screen.
Above I posted a few of different ideas for in game name-tags, feel free to photoshop some user interfaces yourself!
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Something simple, clean, and angular. Complex but not over-done. Easily readable but not boring. Crisp but not jagged. I guess this is just personal preference, so maybe there could be a selection of HUDS of different shapes, sizes, colors and themes (compare a spartan's HUD to an elite's HUD in Halo:Reach) for another dimension of in-game personalization and accessibility. You likey or you no likey?