Assuming that you have a Softcane/nobile type Dendrobium.... the best time to take the keikis off and pot them up is spring. This is because this type of orchid is about to go into rest mode in Autumn and will probably not grow any new roots if repotted now. Tag should read Dendrobium Dream 'Ace'.

Dendrobium Dream is one of the Yamamoto hybrids; it should be very, very easy to keep growing and blooming. Good score!
If it were my plant, I would leave the keikis on it pretty much indefinitely. If you repot or put it in a basket (a very small pot or basket) when blooming is finished next year, if the keikis really bug you, you could tack them to the edges of the pot/basket with a hairpin or something. I'd just leave them, they add to the plant's lush, crazy look.
Someday, when you go to a plant swap (or find somebody on this list to swap with), those keikis will be prime trading material. Easy to grow, blooms small.
The Yamamoto site recommends a slight lessening of water in winter, with no fertilizer, and high light levels. This type of hybrid generally will not lose all of its leaves over the winter, but if it does, don't toss it! It's fixin' to bud out.
Have fun - Nancy

Thank you so much for the responses. The orchid forum is a great source of information.I think I will leave the keikis on the plant. The Dendrobium Dream 'Ace' is in a 6 inch wooden basket and is very full and healthy.I think Carmelas Orchids is a great place to buy orchids. Good to know the dendrobium is a Yamamoto hybrid. Thank you both for the info. Sincerely, Diane Keith