I like to swim too so I only run every second day (3-4 days a week) and I swim 2 times, my rest day usually is either Monday (it was today) or Wednesday. I do my long runs on Saturday or Sunday

My schedule is right now:

Monday: hills and strength or plyo
tuesday: 2 runs- morning/ evening
wed- active rest
thurs- speed/fartlek plus strength
fri- easy run plus yoga
sat- long run
sunday- full rest (though I admit sometimes I lift a little here if I didn't fit it in during the week)

My rest days rotate depending on weather and schedule. Right now i have 2. My weekly schedule:

Mon-fri - 3 days of doubles, am/pm split
1 day of either hills, 800s or tempo
1 rest day
Sat - swimming with 4 y.o.s and possibly my long run
Sun - Long run if i didn't do it Saturday

i fit yoga and body weight strength where ever I can.

I've pretty much stopped taking rest days and just cross train instead but when I did take one it was the day after my long run.

I haven't really needed one lately, but I don't run hard day-to-day and use races as my speedwork. So far, so good.

I'm following Hal Higdons Half Marathon Intermediate.
Mine are on Fridays.
I plan to do yoga and other stretching. Plus foam rolling. And potentially my physical therapy exercises

Day after long runs are usually rest days for me

I follow Hanson's and run 6 days a week, so my rest day from running is Wednesday (long runs are on Sunday), so right in the middle. It's actually between speed work Tuesdays and tempo run Thursdays.

I don't have a certain day that is my rest day, though it is usually mid-to-late week that I take it. It just depends on what day I feel the most tired. I try to follow my body's queues on that. If I still feel energetic and awesome on Wednesday, I'm not going to take a rest day just because it says so on my calendar, but if I do speedwork on Thursday and am feeling sore the next day, I'll make Friday my rest day that week.

I run 6 days a week, and I have the same types of running work outs every week, but I don't always do them on the same day each week. I know some people have, for example, every Tuesday being Hill Day or whatever, but for me, as long as I get my Hill Day in at some point in the week, I don't care what day it happens on. It keeps my weeks from becoming the exact same thing, and helps me stay less "bored", especially when I start increasing my mileage. When my running routine is always the same especially when I'm logging a lot of miles, I get mentally burned out, so I am the type that needs to constantly change up my routes, my terrain, the time of day I'm running, or even just do things like buy new shirts to "break in"... something. Sometimes a new pair of socks is all it takes to motivate me through a sluggish week! ^_^

When I take a rest day, I make it a true rest day (as in no strength training, no cross-training... I walk places because I live downtown, but that's it. No other exercise allowed LOL! Honor thy Rest Day and keep it holy!)

Mine is also the day after my long run.
Typical schedule is:

M - Rest
T - Run/Strength
W - Run
Th - Cross/Strength
F - Run
Sa- Run
Su - Run