<<Disclaimer: Verify this information before applying it to your situation.>>

4 Categories of answers: It's a good idea; It's a bad idea; I thought it was a bad idea, then I had it done and now I think it's a good idea; here are websites for more info.
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HERE'S WHY IT'S A GOOD IDEA

It will tell you if you have been compliant on your GF diet.  You could be getting some gluten in your diet and you're not even aware of it.  If you are 100% sure that everything you've put in your mouth all year is GF, then you don't need it.  It's just a "self-check".
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If you were diagnosed through blood tests to begin with, periodic testing will help determine if your antibody levels have dropped. If they stay within the normal range, this means you are in fact sticking to a gf diet (that is, not getting any hidden gluten).
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This is the only way a Celiac can tell if they are complying to the GF diet.  Your numbers have to remain negitive.
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I get blood tested every year to be sure that I am staying healed and not ingesting hidden gluten.  It is just a safeguard to tell you that you are really maintaining a GF diet. 
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The test shows compliance with the diet.  Sure you know you are trying to be compliant with the diet but you may be getting hidden gluten.  Over time our systems change so what was a celiac reaction pre-diagnosis may not be anymore.  Each year my celiac daughter has her total blood count, her tTg and a number of vitamin levels check.  Her doctor feels that the tTg is a must but that the other tests could be early warning signs of malabsorption.
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You should have your blood checked every year to make sure your Ttg level is not elevated - sometimes people are not careful with their diet or cross-contamination can occur and some times people don't have symptoms but their levels can be elevated.
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Blood tests help to monitor for gluten sneaking back into your diet (at a level above the occasional slip). Also, TTG can remain elevated in other auto-immune diseases, tipping your doc to keep looking for something that may need to be treated.
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HERE'S WHY IT'S A BAD IDEA

 It's so the Dr. who owns a share of the lab, can make more money. 
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it will tell you nothing.....just puts money in the md's pocket!!!
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I GOT TESTED AND FOUND OUT I HAD A PROBLEM I DIDN'T KNOW ABOUT
The presence of antibodies indicates that gluten is slipping into the diet somehow. I was first retested about a year about (biopsy) diagnosis, and was surprised by evidence indicating I was not as compliant with the diet as I thought I'd been. Helped with the learning curve. Later tests have reassured me that I've got it in hand.
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I didn't think there was any good reason for re-testing. I have been experiencing other GI discomfort so my doctor ordered blood tests as well as upper and lower endoscopy.  All test results showed that there is no evidence of un-healed damage from CD nor anti-bodies indicating exposure to gliadin.  The conclusion from this is that I have been adequately vigilant in gluten avoidance.  That is gratifying.
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My daughter and I are both biopsy-confirmed celiacs.  We follow the diet very strictly and I keep up with the latest news/info. However, this year when we underwent our annual bloodwork we both came back with elevated numbers.  Very discouraging - but at least I know we are breaking down somewhere and I am taking steps to determine where the problem may lie
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I was eating the millet bread from Deland Bakery (which was later found to be cross contaminated) for about a year and never really noticed any symptoms.  My endocrinologist had been following me for my thyroid and was lowering my dose over the two years that this occurred. Suddenly my blood work indicated that I needed my dose raised.  This concerned him and he felt some malabsorption was going on and sent me to a gastroenterologist.   Blood work showed my numbers to be very high.  It took me awhile to figure out which food I was eating that was causing it.    Retesting 3 months later showed the numbers to be coming down. 
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GO TO THIS WEBSITE FOR MORE INFO
http://www.celiacdisease.net/About%20Celiac%20Disease/antibodytesting2.htm

If you go to www.alamoceliac.org and click on Celiac FAQs,  the fifth question is this very subject, along with links to places that tell you why and what you need to know.

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