What good is the "Support" class in Battlefield 3? How do you play it effectively?

First of all. Ammo is important. REALLY important. If you're support, hit 3. A LOT.

Secondly, the Support class is a master of laying down suppressing fire, and can keep people from popping out from behind that corner while the rest of your team moves up, or flanks them.

Thirdly, the support class later unlocks C4's (very handy for taking out tanks and other armored vehicles), claymores (useful for keeping your team from being flanked) and a mortar (very useful for defending an mcom or providing support for your squad).

To play support effectively, all you really need to do is deal out ammo around your team-mates. A support that actually hands out ammo will be noticed by others and commended (my proudest achievement so far is the resupply medal :P). Other than that, keep chokepoints bullet-ridden, and take out any armor that comes along (if you have c4).

All in all, while support may seem like it's got less to offer, it's actually a much more versatile class than any other, able to deal with almost any problem that comes along.

Also AMMO!

The view of the classes you present in the question is way to simplistic.

Support

• Provides ammo. This is especially critical on big open maps with lot of armor. Most people play engineers using up their rockets really quickly;
• Having LMG with 3.4x + bipod, can provide accurate suppression fire at mid distance (upcoming patch is going to improve that);
• On rush maps can effectively suppress enemies preventing them from getting anywhere near m-coms. That can be done either with LMG + extended mags or with mortar (later is going to be nerfed in upcoming patch - 4.8s reload instead of 3.5s);
• Can run up to tanks and destroy them with C4, this is especially effective between buildings.

And BTW you say just "Recon has a sniper-rifle", which is big understatement.

Recon

• Can set spawn point, which is quite important on rush (well placed, can allow whole squad to spawn within defenders' base time after time);
• Can set SOFLAM, which greatly increases effectiveness of Javelins, also allows Javelins to shoot down aircraft;
• Can use MAV to spot enemies far behind their lines. Then Support can pick them out with mortar.
• Can set T-UGS near m-com, allowing defenders to react before attackers get chance to arm it.