What are your best homework assignments?

Would you accept my humble answer as someone who has never been a teacher? (I have, of course, been a student!) I suppose I was at one point your target audience. My favorite assignments were always creative assignments that made me think. My very favorite was to do something that introduced something in drama class. We could do a paper, poem, drawing, etc. on any topic, as long as it had citations and we introduced it whatever the paper's topic was. I wrote a paper introducing Japanese plays and I'm so proud of it I re-read it every now and then. It allowed for creativity, ideas, and of course research.

Is there a way to combine the previous two answers--useful in real life, but creative? Some random ideas: you could have students imagine themselves ten years older, writing an email soliciting a job from the most awesome company they can think of (this can be their real dream job, or something crazy that would make the assignment fun to write, like professional dolphin trainer)--except the company speaks x language. Anything matching up potential usefulness in the students' future use of the language (sure you're having fun writing this crazy letter asking for a dolphin trainer job, but you also had to work in two chapters of vocab words and research the appropriate German salutation for a professional letter) with some leeway for imagination and fun or a challenge. E.g. pen pal letters, or short blog posts, or transcripts for a radio commercial selling some fake/silly product. Or a contest to see which student can make the shortest but most sensical paragraph incorporating all of the chapter's vocab words. Or let the students explore different genres of writing (in addition to job letters and radio commercials, e.g. teen vampire fiction, the principal making an announcement over the P.A., letter to the editor of the school newspaper).

Agreed with all of the above -- needs to allow a student's personal touch, needs to not appear as busywork, needs to still be relevant to your class. I'm not a teacher, still a student (junior in college studying Illustration, more specifically), but I remember my favorite high school assignments being those where I got to show what I knew AND research something that was of interest to me or apply some other skill that I already have to a seemingly-unrelated subject. I love pavane's idea of a letter -- this is a good example. Another interesting angle might be etymology -- I always thought it was interesting to know where words came from, and it expanded both my foreign language and English vocabulary, making it easier to remember what each of them meant. Have students look at the connections between things they know (English words) and where they came from (...pretty much everywhere else). English borrows so many words and word particles... this is probably already part of the Latin class, but introducing it into French, Spanish, and German could be interesting.

Please look into Flipped Classrooms. It makes homework part of the direct instruction, rather than practice on their own (without you around to help). I'm an English teacher, but you're welcome to check out http://www.morrisflipsenglish.com to see how it looks in my classroom. I'd also encourage you to get onto Edmodo (it's kinda like Facebook for teachers) and get into the learning communities #FlipShare, #FlippedClass, and the Foreign Language Forum. They'll have better subject-specific ideas.