Microcomputers for Homebrew Projects?

tengwar asks: "Way back when I was at university, I did a course on microcomputers which went into enough detail to design, build and program a Z80-based system - more or less state of the art at the time. Now that my lecture notes are firmly embedded in the Carboniferous layer, I'd like to have a go at doing this with a more modern chip, and I wondered what's available. I'm not brilliant at electronics, and I liked the way the Z80 peripheral chips integrated easily with the CPU. Obviously I'm not looking to just slot together the latest PC motherboard with the latest Pentium, but I'd need to go for something where the board design won't get too complicated, which probably rules out processors with full 32-bit external interfaces on space grounds. I'm not really concerned about performance, but it would be nice to be able to port a JRE to it rather than working entirely in assembler. Any thoughts on suitable starting points?"