Seeds, sprouts and adult plants can be abandoned. To abandon a plant, you must go to its page. You can get there from your The Greenhouse by clicking the plant image or the "View" button in the classic list layout. After clicking the "abandon" link you will be asked for confirmation (Caution! If you disabled Java-Script in your browser, there won't be a confirmation pop-up), and the abandoned plant will land in the The Wild Garden. This action is irreversible. Abandoned seeds and sprouts can be picked up by other users. However, adult plants are not available for picking up. They continue to exist in some secret place in the Wild Garden, and their pages can still be reached if you happen to know their URL. Experimenting with URLs has resulted in finding some abandoned flowers; their location is specified as "Unknown".
There is a daily limit for the number of plants you can abandon. If you reach this limit, you must wait 24h before you can abandon another plant.
Reference: News - Small changes
You can also decide to trash a seed, sprout or an adult plant. In order to use this option, you must go to the plant's page and click the "trash" button. You will be asked for confirmation (Caution! If you disabled Java-Script in your browser, there won't be a confirmation pop-up), and the trashed plant will disappear from your garden. Its ID will be permanently deleted from the system.
Just like with "Abandon", there is a limit for the number of plants you can trash. After reaching this limit, you must wait 7 days before you can trash another flower.