Your tap water will have particular properties depending on where you live, the source of your water, and whether you have some sort of water softener or filtering system.
My tap water, for example, is from the public system and is considered 'hard' because it has a high mineral (calcium and/or magnesium) content.
If I use tap water consistently on certain plants, I can see white rings of calcium deposits sitting on the soil surface; this can change the chemical properties - such as the pH - of the soil which can affect plant growth.
Softened water has higher levels of salt than plants prefer, and these salts can build up in the soil.
I've never seen the chlorine in public water causing any ill effects on my plants, but if you have sensitive house-plants you can let chlorine-treated water sit out for 24 hours to let the chlorine evaporate.
As long as you live in an area that isn't subject to extremely acidic rain, rainwater is preferable because it's missing things like excessive minerals or disinfectant chemicals.
gardening.stackexchange.com/users/133/Shanna
If your plant is not special plant such as carnivorous plant, any water from the tap is okay.
The fact is tap water may contain different things such as chlorine, and a lot of different minerals.
My plant is drinking water with chlorine day to day, but they are thriving.
In the end, rain water maybe good, but who knows what is inside the water because the contamination from human activities such as car driving and industrial plant releasing exhaust fume from the chimney.
Check this link , and this too.
You may want to have your own judgement.
I think rain water and tap water are both okay in some extent, on the other hand, distilled water is not really that good because most of the minerals are lost.
I prefer tap water ,it is cleaner because chlorine kills bacteria.
gardening.stackexchange.com/users/140/lamwaiman1988
Rain water is always the better choice.
City water can contain elements that could eventually harm the plant.
When the rainwater is unavailable the tap water will be just fine.
gardening.stackexchange.com/users/108/Gardening Directions
Sweet peas, garden peas and broad beans prefer rain water.
Although they still grow when watered with tap water the results you get from watering with rain water are vastly improved.
Chlorine and other substances in mains water inhibit the uptake of nutrients and thus reduce plant growth and health.
gardening.stackexchange.com/users/1079/Kate Jackson
Rain water has a neutral pH.
It's usually softer than tap water and soaks in the ground deeper than a hose watering; people don't water long enough to equal the soak of a good rain.
There are particles picked up in the atmosphere during a rain which offer nutrients to the soil that tap water does not have.
gardening.stackexchange.com/users/6832/Richard
I can understand what many are saying here, but to me rain water is best.
I live in the country and no matter how much water I give my plants they won't grow as much as they grow after a rain soak.
My best guess is that plants may like electrolytes or charged particles more so than we understand.
I have seen plants that have not grown for a few years of tap water, grow two or three fold after a good soak of rain water.
gardening.stackexchange.com/users/11978/Nef
If you are growing from seeds I would definitely use tap water.
This is clean water and free of any microbes, bugs etc., that may cause damping off or rotting etc.
Rain water from water butts would be fine on most outdoor plants.
Rainwater is also as others have said is generally softer than hard processed tap water, so things like orchids or acid loving/lime hating plants would prefer rain water.
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Rainwater is generally better.
Chlorine, fluoride, bleach and such, which are in a lot of city water, may not harm your plants in the drinkable amounts, per se, but they certainly may harm the beneficial microbes in your soil, which will reduce the benefit you would gain from those microbes (which may be considerable).
I find that my tomato plants last year preferred filtered water to regular city tap water, probably for this reason.
They required less water and grew better when I filtered the water.
I imagine rainwater is similar to filtered water.
Rainwater is probably pretty much devoid of minerals.
It may contain chemicals via pollution, however, and your guess is as good as mine as to what those chemicals will do to your plants and soil microbes.
Well water, without chemicals added, has the potential to be better than rainwater, depending on your soil and the composition of the well water, because your soil may need those minerals.
On the other hand, the minerals in the water may have come from the above soil in the first place, in part.
gardening.stackexchange.com/users/7111/Brōtsyorfuzthrāx
Water from a hose is usually delivered at a faster rate than rain falling on say pottered plants.
Usually all the rain falling on a potted plant remains in the pot but the outflow at the bottom of the pots with hose water will take many leached nutrients with it.
Another factor is the build up of hard deposits on the parts of the plant which take in the water when tap water is used.
Note this similar effect also happens when a car is "washed" with rain how clean it gets ...
remember the scale build up on taps!
gardening.stackexchange.com/users/15129/Hosepipe Nyge
Is it better to water your plants with rain water collected in  water butts ? I mean is that better than water straight from the tap?  And is it just a matter of temperature (presumably plants don't like to be soaked with very cold water (as mains tap water is)? Or are there other factors?  I'm interested in the effects on plants, rather than the separate issue of the cost to the planet of using mains tap water.  See also  Does water temperature affect plant growth? .
Is rain water better than tap water for plants?
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<watering><rain-barrel>
gardening.stackexchange.com/questions/700
gardening.stackexchange.com/users/99/Tea Drinker
Your tap water will have particular properties depending on where you live. This can change the pH of the soil and affect plant growth. Rainwater is preferable as it doesn't contain any chemicals. Your tap water will have particular properties depending on where you live, the source of your water, and whether you have some sort of water softener or filtering system. Chlorine and other substances in mains water inhibit the uptake of nutrients and thus reduce plant growth and health. Also softened water has higher levels of salt than plants prefer, and these salts can build up in the soil. Rain water is always the better choice as long as you live in an area that is subject to extremely acidic rain. S0: Rain water has a neutral pH and plants such as weet peas, garden peas and broad beans prefer rain water.
Your tap water will have particular properties depending on where you live, the source of your water, and whether you have some sort of water softener or filtering system. Chlorine and other substances in mains water inhibit the uptake of nutrients and thus reduce plant growth and health. Also softened water has higher levels of salt than plants prefer, and these salts can build up in the soil. Rain water is always the better choice as long as you live in an area that is subject to extremely acidic rain. S0: Rain water has a neutral pH and plants such as weet peas, garden peas and broad beans prefer rain water. Both rain water and tap water are both okay to some extent, on the other hand, distilled water is not really that good because most of the minerals are lost.