Yes my rabbit eat veggies. A rabbits diet should consist mainly of fibre, so hay/grass should be plentiful. Rabbits graze so do need food at all times and should never be restricted, this can cause the guts to slow and this is a very serious condition particularly in youngsters. However its best to limit the amount of pellets they eat as this is where the problems with obesity etc come in.
There are generally two different types of rabbit food: the extruded pellet type, and the muesli mix. Of the two, the pellet one is the better one to go for. Muesli mix can encourage selective feeding-this is where the rabbit choose just the nicer (often sugary and unhealthy!) pieces, and leaves the more nutritious ones. The bowl is then topped up so again the nicer bits are consumed leaving more of the better pieces. With pellets you don't have this problem as all pieces look the same. It can be difficult with some bunnies to change over from a muesli mix to pellets as they don't find it as appealing!
With any pellet/mix, feeding too much can lead to obesity and dental/gut problems. An egg cup amount of pellets is enough really for the average adult if hay is unlimited. You can of course still add some fruit/veg to the diet, but mainly fibre should be aimed for.
