Slice them and put 'em in a mayo, sugar, and pepper based sauce.
(It’s a nice alternative to the vinegar based sauces: I normally have half the cuke cut up and put into the vinegar sauce, the other half cut up and placed into the mayo based one.)
Cut 'em up and place them in a stew or soup.
Get some of the props meant for Mr. Potato Head and use them on the cuke.
Get three or four smaller ones, and a portabello mushroom and make a veggie table/stool.
Use them as play-swords.
Use them to play with a cat who’s in a playful mood and save your own skin from gaining unneeded ventilation.
“Concombre Fatigue!” My mom takes slices of cucumber and soaks them in vinegar with a little salt and pepper. Shake it up really hard, or just leave it long enough for the cucumber to get kind of mushy, and eat. Its good!
Mention of India and tzatziki in this thread brings to mind a nice Indian side dish, Cucumber Raita. Mix yogurt, finely diced cucumber, and a little ground cumin. Simple and goes great with spicy curries.
Cut into chunky sticks, add a little salt, lemon juice and pico de gallo chile (ethnic section). So yummy you’ll lament the many years you’ve wasted sans this treat.
Also, they make a reasonable, though slightly juicy, substitute for potatoes when you’re making potato prints.