I have several orchids. Some of them produce root systems from the stems and produce new plantlets .. My question is can I cut these plantlets away to replant?

Yes! I have propagated quite a few this way.

Divisions & back bulbs

Some orchids grow by developing new growth from the base of the plant. After several years they may have 5, 6, 10 or more growths. We may subdivide such plants to get two or three out of the original one.

Often the older growth or old pseudobulbs of these plants do not do anything but if we remove them and plant them separately they will generate new growth.

Again as for the previous methods where plants were propagated by using tissue, or the fower tem, plants resulting from divisions and backbulbs are also entitled to be recognized by the same variety name as the original plant from which the growth or back bulbs were removed. The resulting plants will be identical to the plant we divided or from which we removed the pseudobulb(s).

Keikis

Some orchids, mostly Dendrobiums, are notorious for producing keikis which is the Hawaiian word for “babies”.

Occasionally Phalaenopsis will also produce keikis. Some, usually species, do it because it is programmed into their genes, others do it when they are exposed to high temperatures while they are developing a flower stem.

Keikis will develop leaves first. Eventually they will develop roots. When roots have reached about an inch in length we can remove the keiki from the mother plant and plant it in its own container.

Keikis will be identical to the plant they were removed from and are also entitled to be recognized by the same variety name, if any, as the plant from which they originated.

Source: www.orchidsusa.com/1Introduction.htm#1.4Howorchidsgrowinnature

I have several orchids. Some of them produce root systems from the stems and produce new plantlets .. My question is can I cut these plantlets away to replant?

Yes you can. The best time is before they start growing again (rainy season). I had most successes when I did the propagating so the small plants had some time being dormant and then could grow in the rainy season. It is not good to do the propagating shortly after the rainy season.

Thanks both. I did suspect it was so, but wasn't sure. I only ever grew weeds in the UK. That's weeds not weed.