Many modern F1 varieties e.g. Sakura F1 are resistant to the most common leaf diseases such as Leaf Mould (Cladosporium) and Tomato Mosaic Virus (TMV) (Gardener’s Delight is NOT resistant to TMV). Powdery mildew can also be a problem in some years.
If you have a small greenhouse and always grow your tomatoes in the same place, then there can be a build up of soil-borne diseases such as Fusarium (wilt; crown and root rot), Verticillium wilt and Corky root rot. You can get round this either by not growing in the soil or by using grafted plants: see To graft or not graft?
Did You Know?
British Tomato growers use an army of over 40 million beneficial predatory bugs called Macrolophus in summer to keep pests out of their crops, reducing the need for chemicals.