• Lumps and outgrowths on the stem, usually near the bottom: These are likely to be root initials, which often cause alarm to gardeners, but are in fact harmless. Tomatoes produce roots from their stem very easily, and this is usually no cause for concern.
• Dead, rotten patches on the stems: A disease called Didymella stem rot (caused by the fungus Didymella lycopersici) can attack the stems of tomatoes causing brown, rotted patches, at any height but most often at the stem base. Affected plants can wilt and die, and should be removed immediately to prevent infection of the remaining plants.
• Brown patches on the stems: Tomato blight can cause brown patches and decay on both the stems and leaves. See the link below for further details.
• Wilting with staining inside the stem: This may be caused by the diseases Verticillium wilt and Fusarium wilt. See the link below for further details on Verticillium wilt.
• Fluffy grey or white mould on the stems: This may be caused by Sclerotinia or grey mould (Botrytis cinerea). See the links below for further details.

Links

Tomato blight
Verticillium wilt
Fusarium wilt
Sclerotinia disease
Grey mould

Root initials on the stems are encouraged by humid conditions. Root formation on the stems also seems more common when plants are under stress. Hormone weedkiller contamination also sometimes leads to stem root formation, but the additional effects of this contamination on the foliage are more dramatic and are usually noticed first.

Root initials are not very significant, but they might indicate that fine-tuning of cultivation, especially watering methods might be needed. Keeping the stems and foliage dry when watering should remedy the problem, and will also help to prevent tomato blight.

Some of the diseases that affect tomato stems can persist in the soil. Changing to a system of growing in grow-bags or in pots will prevent these diseases. There are no soil fungicides or soil sterilisers available to home gardeners. Removal and destruction of all infected material is also a wise precaution.