Were there any Intel 8080 based home computers?
Yes, but the number is rather small, as at the point when the idea of a home computer as we know it today (and you describe) became popular, better 'versions' of the 8080 were already available, most notably the 8085 and Z80. Importantly for low cost computer design, they did away with -5 and +12V supply, thus simplifying power supply design a lot.
Some on this list may be
- SOL 20 of 1976. As early as it can get for a desktop computer.
- Compucolor II of 1977. A prototypical home computer due to its consequent consumer design.
- Interact Home Computer of 1978. Already quite late for an 8080 machine and mainly sold even later by liquidators. It might not fully fit your needs as the BASIC needs to be loaded from tape.
- Micronique Interact of 1980 (!). The same machine, but now made and sold by a French company.
- DAI Personal Computer of 1980. Originally designed to be the (European) TI home computer. Eventually the most ambitious machine of them all. Quite a great design for back then.
As said, the time of the 8080 for new designs was already long gone when home computers became a thing, so these are rather oddities - at least in the west. History is different within the former east bloc as their hardware/CPU development lagged behind (due to cloning), while information about microprocessor applications was ready available (as Wilson already mentioned).
There are 8080 clones like the Russian КР580ВМ80А (1979) or the Polish MCY7880 (introduced rather late in the early 1980s). All of these machines were rather plain 8080 systems. Starting from Kits like Micro-80 and Радио-86РК all the way to quite modern, feature-rich systems like Vector-06C and Orion-128. The landscape was at least as diverse as in the West, if not more. All with a certain time shift.
More relevant to your task would be the rather large selection of software these machines featured, as each had (in their countries) a quite strong fellowship. On the down side, it's usually in the local language with no English documentation and hard to find, as relevant web pages are also in the same language - Google Translate is only a help after a relevant page is found.
Of all the Eastern 8080 based machines, the Czechoslovakian Tesla PMD 85 is worth a look. Despite its name, it's not an 8085 CPU, but their own MHB8080A (the semiconductor division is nowadays part of ON Semiconductor). The machine is not only remarkable for its huge amount of available software, but also for having evolved over the years from B&W to colour and into several spin-offs like the MATO - while the basic hardware is rather straightforward.
An oddity here was the otherwise usually advanced East Germany. While following the Intel lane (unlike Bulgaria), they skipped the 8080/8085 steps and went directly from i8008 (U808) to Z80 (U880) - which is a story of its own. Thus even their earliest kits (LC80) and home/small computers (Z9001/HC900) used it from the start.
Then, why not use using some Hungarian machine? Sure, all (genuine Hungarian) machines I know of (Mikrokey Primo, Triton, Aircomp) are Z80-based, but it should be fairly simple to adjust the design to work with an 8080 - especially in FPGA, were the RAM is embedded anyway. After all, you should have much less hassle to dig up documentation and software for these, shouldn't you? :)) Of course, you may need some backward translator Z80 to 8080. So not much fun.
An only slightly different way would be switching the 8080 for an 8085, like Curt sugested. In most respects, the 8085 is only a hardware update to simplify system build. Only two official new operations were included, which in addition almost never got used in full. Of course it had some lesser known but quite handy extensions.
While I can't think of a plain 8085 home computer, the CPU is most notable for being used by the quite well selling Kyotronic 85 series - usually disguised as NEC 8201/8300, Olivetti M10, Tandy M100/M102. They are stand alone, have BASIC, lots of other software (in ROM and loadable), are simple (all parts obvious). Only TV out is not by default but needs an extension. Now, doing an all-in-one Kyotronic would be a cool project I'd love to see - or may even join.
Conclusion:
I'd like to build an FPGA replica of a home computer based on the Intel 8080.
If you want to have some software to choose, you may settle for the Interact as the basic documentation is available in English (more advanced and most software in French) or any of the eastern (and learn Czech, Russian, ...)
If you want hardware that allows to build your FPGA system in incremental but complete steps, the PMD 85 is your choice.
If you want a well defined and satisfying system with lots of extraordinary features and few but awesome (system) software, go for the DAI (some French/Dutch might be helpful).
If you want to have something with a huge user and software base, maybe even useful today, go for the Kyotronic 85 (no Japanese required) .
