How can you tell when you need to replace tubes?

Can I tell by listening if I need to replace power tubes on my amp?

Should I have the tubes tested regularly?
As a matter of fact should I test all my amp's tubes? I currently own an AES Super Amp MkII with EL34 output tubes and 6SN7 front end tubes.

I have a basic meter. Can I use this to test the tubes, and what values am I looking for?
When I used tube amps this question always bugged me. Being bugged distracts from musical enjoyment. Tubes degrade gradually, so it is not easy to recognize how bad they have gotten.

The best suggestion I have heard is to keep a spare set of new tubes on hand and plug them in from time to time to see if they make a difference.
You don't need to test tubes to see how they are performing unless you have a SOTA system and are anal about maintaining that sound level.

First, I agree with Eldartford, except it can be a PITA to put in new power tubes, rebias them etc. Small tubes is no big deal. One of the upsides to doing this is the friction on the pins on the tubes with the clips in the sockets will help clean them up.

Signs of tube demise is usually signalled by;

1) Noise (most often heard in the small tubes);
2)A dulling of tone. The latter is hard because it comes on very slowly, but IMHO as long as you still love the sound don't worry about it; and,
3) Make a note (tape it on the back of the amp) identifying when you last changed tube sets. Depending on how hard you are driving power tubes you can expect 1500 to 3000 hours. Small tubes are usually good for anywhere from 3000 to 10000 hours depending upon amp design. You could tet them if you had a tester, or you could then plug in a new set to see what you are missing, if anything.

Hope that helps a bit.
A couple of years back I picked up a Superior TV11 tube tester on eBay for $40 or $50. Not the fanciest tester in the world (it is just an emission tester) but it works for my purpose.

If you decide to buy a tube tester I would recommend you educate yourself about the different types and watch the auctions so you can bid intelligently.
With break-in often reported by audiophiles to be up to 1000 hours and power tubes lasting about 3000 hours it would seem to be a critical question that demands a precise answer. However, precision audio is a bit of a mystery - like cooking a great meal - sometimes it turns out just fantastic and other times it just doesn't cut it - even carefully following the same recipe.
I did not realize that tubes take 1000 hours to break in until I experienced it my self. I can say it has been that long, but the tubes sounded harsh and cold at first. Now the EL tubes sound very detailed with good layering and seperation, plus there is no harshness or distortion like at first. I though EL tubes were not very good until many hours were on them.