Here is my take on this type of class: The benefits of infant classes are, building physical, emotional and musical bonds with your child, giving infant and toddlers a chance to interact with other children their age and (in some cases) learning American Sign Language and Baby Sign.
The curricula, from my experience, are well thought out by trained educators, the percussion instruments, stuffed toys and class materials are well made and age appropriate (jingle bells are in baskets so no little lips or tongues get caught), and the music can vary from class to class. There tends to be a lot of super-cheesy kid sing-alongs which I abhor, but I guess infants respond to young voices. Gymboree has a partnership with Putumayo music which provides them with great music from around the world.
Here are my caveats: Most of these companies are big national chains. Though the teachers are provided all the materials and lesson plans, the class is only as good as the teacher running it. Typically you can try a class for a reduced price or for free (look online for coupons!). If you or your kids don't respond to the teacher, keep looking. With that said, the location is only as good as the management. I left Gymboree in Miami three years ago after not being paid for my time (I'm still waiting for my check!), but it's still one of the top retailers of kids' clothing nationwide and scores of people enjoy their classes everyday.
At the end of the day, this was the best thing for me. I take pride in developing my own curriculum, and I found the rigid framework to be too constrictive (plus I wasn't allowed to encorporate my songs or bring in my guitar, banjo, drums, etc.). There are lots of studies that show that these infant and toddler classes can improve body awareness, motorskills and musical acuity. The Mandarin Chinese have 70% higher rates of perfect pitch because they grow up learning a pitched language where the tone of a word can change the meaning. However, I always try to warn against the "Baby Einstein," myth. Infant classes will not get your kid into Harvard, nor will they be guaranteed a headlining bill at the Royal Albert Hall. It's the same thing I see in preschool where parents expect their kids to be reading and writing even if they can't use the bathroom or dress themselves on their own (I can tell you which skills their Kindergarten teacher is expecting to see!). These types of classes are mainly for fun, so go and enjoy yourself, and wear clean socks cause you may have to march around in them!
Update:
Here's what my mother (Anne for those of you who follow the comments) had to say:
"I would say that if you have the time, try it and see what you think. Use your judgment. I did some little music and Mommy and me gym classes with you kids at the Y when you were wee ones. My only caution is not to get suckered into having to do "classes" with Miles when he's little. We have parents whose preschoolers are in dance, gymnastics, soccer, music and so on. One little girl goes from school to dance and then swimming all in one day! Too much! Kids need time to be home and chill. That being said, if you find the classes provide and opportunity for some quality time with Miles (meaning that he enjoys it, too), and a chance to connect with other young parents, then great!"
Kid Quote of the day: "Nicholas [a classmate, not me], your mom does too much for you. You should feel lucky that she even bought you a birthday present!" ~ James (age 8)