I miss the different kinds of procedural noise textures.
My thread 100+ Free Cycles Procedural Textures illustrates how that has not held me back, in terms of creating many different things from the one noise and other basic procedurals Cycles offers.
Still, some different noise models would be nice. Even nicer would be if all BI procedurals could eventually be ported to Cycles.
I do miss halo materials, including all the Rings / Lines / Star Tips and Flare options. Those were special.
I miss the simple wireframe material. That was so useful for technical and artistic purposes.
I miss negative shadow lamps, hemi lamps, and the general ability to use This Layer Only and to be able to toggle on/off Specular and Diffuse influence.
I miss the quick ability to select a Diffuse Shader Model (Fresnel, Minnaert, Toon, Oren-Nayer, Lambert) and Specular Model (WardIso, Toon, Blinn, Phong, CookTorr).
As I often work in non-photorealistic (NPR) manners with Blender, those non-physically-correct models were often useful and artist-friendly.
I miss the simple and quick Shadeless material option.
I miss the simple toon lines option. FreeStyle + Cycles can take forever, while BI just worked.
I miss the simple Mirror with built-in Fresnel and Blend option with custom depth (which I often used in varying ways to expedite renders).
Now, I have worked intensely since last year to find work-arounds for all of these things as well as discovering strange, new methods in Cycles, and I have succeeded, to the point I can now comfortably proceed without Blender Internal. But that involved hundreds of experiments, attempts, and failures - a lot of effort which helped inspire my Cycles procedural giveaway thread above.
Still, its speed, artist-friendliness, and NPR abilities are nothing to discount or dismiss, and I think it would be amazing and useful - especially for compatibility purposes with earlier .blend files - if Blender Internal could be externalized as a renderer and provided as an alternative to Cycles and Eevee.
As a programmer, I know that represents a lot of work, and people can always download earlier Blender versions, but, I never exhausted BI’s potential (and those who know me know I tried), and I’m sure some users and digital artists out there might actually prefer it, especially if they lack sophisticated hardware / GPUs.
It wasn’t until I upgraded my GPU and got a new laptop that I was entirely able to even begin to use Cycles, and that was as of last year, even as I’ve since found various ways to make Cycles render faster.
One other often overlooked aspect of Blender Internal was its modest hardware requirements. Yes, it lacked Cycles-style GPU acceleration, but, it often did not need that and was more than adequate for various projects, especially those not requiring hardware-intensive PBR.
Trying 2.8 on some of my hardware, I notice that certain GPUs are not even recognized (even with latest drivers).
I appreciate 2.8 is bringing with it even more changes (e.g. Collections vs. layers) and exciting possibilities, and I look forward to doing even stranger newer things with that 
Blender Internal, though, was the familiar brush, the dependable pencil or pastel, the always ready clay to me: a simple and most effective tool capable of so much, where, at some point, not long after first learning it, I could focus almost exclusively on the art.
Cycles, like BI, is now a dependable friend to me, and I can ask of it whatever I wish, as long I as keep up my end of the bargain and am willing to work at it. But I do find myself wishing Cycles had less of a learning curve.
Despite the variety of styles I worked in over the years, I almost never used nodes-based materials in BI. Having to use nodes for every single material in Cycles is a chore, compared to BI’s near instantly selectable results.
I often hear Eevee is effectively a replacement of BI, but, in my early experiences with Eevee, I find it presently lacks the ease of BI in terms of simple materials and lighting. Eevee is more Cycles than BI by design, so I understand and appreciate the technical distinctions there.
With great determination, I’ve mastered Cycles at this point. Eevee’s appeal to me is in its realtime rendering ability. If that could be pared with the ease and pro-artist aspects of Blender Internal, I think that could be amazing.
I love Blender in all its forms, and I’m grateful for all those who make it possible.
My main purpose in this post, though, is to attest that, after many years and public projects with Blender Internal, I believe BI still had lasting relevance and potential for reasons that transcend technicalities (e.g. physically correct renders).
And, it’s just nice to have choices - to be able to select the render option most optimal for your situation and desired end-result.
BI’s artistic and rebellious NPR spirit can live on, I think, if allowed, and perhaps, at least, there are aspects of it which, upon further reflection, could, at some point, find new life within Blender 2.8+.
Thanks again - and the highest respect - to all the coders and Ton for giving us such amazing tools to work with! Your work is appreciated more than you will ever realize!