Wow, cool!

Those are called adventitious roots. They tend to grow when the plant is exposed to really wet/damp conditions, so if it's been raining a lot where you are, then that's why they're appearing. They don't harm the plant or anything, so you can leave them without any bad effects.

I've heard that a lot of adventitious roots can indicate a compromised or cramped root stock below soil, but I've seen them form on even the healthiest of plants. Either way, your plant will be fine.

Agree. It is very common and assuming the plant is in a big enough container so that it isn't rootbound then they pose no problems. As mentioned their appearance is an indicator of overly wet conditions or a rootbound plant. If the wetness is due to the weather you can't control it other than to insure well-draining soil and make sure you don't over-water. If other symptoms of stress develop I would suspect the plant may be rootbound.

Dave

I'd take that sucker off and stick it in another pot - bonus!

if we place a vertical round net filled wit soil and compost near tomato plant and if we bend the stem to the vertical round net , will it produce side roots and stick to it