Rear derailer suddenly "sticking"?
 

Up until last week (last Wednesday to be exact) my rear derailer and shifter have always shifted up and down perfectly. Never had any issues. Now suddenly it seems like it's sticking a bit. For example I'll shift to a smaller gear on the rear cassette (small lever under my right index finger on DeoreLX 8-speed rapid-fire shifter), and it takes a few crank revolutions before the chain actually drops down to the smaller gear. Is this just a matter of needing some lubrication? Where exactly should I apply lubricant, and what type?

Clean and lube can't hurt. The chain, cassette, and derailleur get crud built up on them over time, and the new systems are real picky when it comes to tolerances and all. Gummed up parts don't help in that regard.

If your drivetrain is clean, check derailleur cable tension.

how old is the bike?

My first suggestion would be clean and lube chain and cassette. If that doesn't help, or you take the cassette off to clean it, then you will want to play with the cable tension.

Cables have a tendency to stretch over time, not suddenly as you suggest your issues came about, so I would guess the chain is gummed up with muck causing poor performance.

The best place to start is the housing loop that connects to the Derailleur. Pull the housings out of the stops and slide the housing away from the derailleur and clean off the cable (you may want to add a very small amount of grease on the part of the cable that is usually inside the cable). If you noticed some resistance when you slid the housing than this should solve the problem. Repeat the same procedure on the other housing pieces or replace the cable. Check derailleur housing for kinks or cracks and replace if necessary. If you want re-use the housing pieces, you can slid them off the cable (dis-connect at the derailleur) and flush them with WD-40.

RD being reluctant to upshift or downshift is a typical symptom of incorrect cable tension. Or, more precisely, it is a symptom that indicates that the indexed positions of the RD are not aligned properly with the actual cogs. Use the barrel adjuster on the RD to restore the alignment. Usually, you can achieve perfect alignment by simply looking at your RD from behind and twisting the barrel adjuster left and right until you find the point where the chain is aligned with the cog.

In your case the RD is slow to upshift. This is actually an indication of the cable being too short (overtensioned). Someone might have played with the RD barrel adjusters without your knowledge and overtensioned the cable. There's also a possibility that the cable is actually overrelaxed and all gears are shifted by one. In any case, the best idea would be to perform the full readjustment of your RD. First see whether the very highest gear (smallest cog) is indexed properly. Then proceed to fine-tune as described above.

check the derailer hanger ,it might be bent .

Sometimes a kink in a cable can slow things down just enough to throw off your indexing. Has this bike been on a full rack or in a car with other bikes recently?

When something like this happened to me last winter, it stopped after 10 miles.
That was when the last strand of wire broke off the cable stop, and the cable pulled out of the brifter.

I think I got it fixed up. Seems like the barrel adjuster did the trick. I took a video with my iPhone before the adjustment. If you watch the shift just as the camera moves towards the rear, you can see the chain seeming to almost jump to the larger gear before going to the smaller. It sounds like it's changing 2 gears when in fact it only changes 1 gear. If you count it's the shift from cog 4 to 5 (1 being largest, 8 is smallest).


And in case you're wondering, I'm holding the phone in my right hand, turning the crank with my left, and working the shift lever with my toes :p