Have you any idea what type of soil you have? Rhododendrons need an acid soil. If you don't want to bother testing it have a look at other nearby gardens for two things - First, do they have rhododendrons, Azaleas or Camelias that look healthy? Or if there are hydrangeas what colour are the flowers? If most are blue then Rhodos should be OK, if most are red or pink choose something else. (Hydrangeas can change their colour according to the acidity of the soil so they are a good indicator) You won't find an evergreen shrub that flowers over the spring and summer continuously though.

How high do you want it to grow? some will get a lot bigger than others.
If you want something bright all year you could look at one with variegated leaves instead. You could look at Ilex Golden King, which will also have red berries if there is a male holy nearby, or Eleagnus Ebbingii - several varieties with gold variegations but you have to be careful to remove any green branches that appear.

Otherwise you will have to chose your season. Most evergreen shrubs flower in spring or winter.

How about viburnum tinus which flowers from October through to April? This is one shrub I reckon should be in every garden.

It certainly does but not very colourfully - and in summer its just dull green? For all year flowering you really need more than one shrub.

I agree Stera, but after about three years (when it has got established), you could plant a small clematis to ramble over it. 'Arabella' would be suitable and flowers for most of the summer.

No flowering shrub flowers for longer than 3-4 weeks maximum, though some produce the odd flower later on. You might be better off choosing something which has evergreen, decorative leaves, maybe variegated ones, because that's what you'll be looking at for 11 months of the year. Viburnum tinus does produce flowers at irregular intervals, but it's not terribly interesting, nor are the leaves particularly riveting to look at - it's also quite prone to infection by Viburnum beetle.

The other option, as Steragram suggested already, is choosing two shrubs which flower at different times, but that choice depends on how much space is available and how much sun the area gets. Or choose a berrying shrub, if its not in deep shade - then you'll have flowers and berries to look at later (pyracantha if you don't mind large and prickly, or Cotoneaster lacteus if there's room for its arching growth habit)

Viburnum Tinus, I have two. Fast growing, evergreen and most importantly, it looks after itself, as well as takes well to pruning.

I wouldn't depend on the viburnum for my only shrub though, especially If I wanted some showy blooms.But its a brilliant suggestion to grow a clem through it - might just do that myself, thanks!