What are inexpensive ways to update the look of cabinets?

Remove any dated bits and pieces such as tiny balconies, corner units and any edging which date them. If you had a floor corner unit take it out and cut down the worktop so you have a rectangle. If it needs some trim you can buy iron on wooden trim or metal which you need to glue on and may have to shape slightly so you have no hard edges and generally sand the trim to make it neat and tidy. You can cut the wooden trims with scissors or sharp knife and the metal with hacksaw.

Measure the handles and replace with something more contemporary. If you have 70's cupboards ( like mine ) they were just plain white anyway and I can live with them. The difference paring things down can make is quite astonishing. If you have a horrible colour you can't live with, get some all in one kitchen cupboard paint, sand the doors well and paint. You don't need to take them down to do this and i would use a small paint roller. Get a few different rollers ( they are quite cheap ) and try each one out on a piece of wood to see which texture ( if any ) you prefer. If you are using a brush and want a pristine finish you will have to check out Youtube to see is anyone is showing how to paint with a brush as it would take me too long to explain.

If you are a shabby chicer just slap it on with a large brush and then roller over it with a dry roller. or you can scrub the paint on using an old brush. Use a base colour and a top colour letting dry between coats and make sure you do not cover all the base coat so some shows through. Your brush should be almost dry of the paint itself so just put some paint into a saucer and dip the brush there and take off excess on piece of newspaper. Try your technique out on a piece of wood first so you can judge how much paint gives you the desired effect. The dry brush tech.can give a nice cloudy finish. Good combinations to use are pink and sky blue, yellow and purple

orange and green ( I don't know why this is popular as it is a combination I hate ! ).

Or make it look like driftwood planks ( using blues, greens and white )

You could use driftwood to make handles. You could cover the doors with bamboo table matts cut to size and edge with split bamboo canes. I have seen this done and if it suits your general theme why not ?

You could cover wth doors with vinyl table covers cut to size. This can be bought by the meter so esay to measure up. You can stick on with any waterproof glue and can fold the fabric around the edges like a book and cover the innner doors with a piece cut to size which covers the overlap.

I have more ideas but hope that's enough to keep you going or spark your own imagination. Good Luck.

Painting them, or having the doors replaced if the cabinet boxes are in good condition. If the placement is wrong, check styles and prices at Ikea.

Strip the finish and refinish. Put on new handles. Paint them.

there are many paint effects you could try; they are not difficalt; combine with decopage as Carmel suggested;

Have you tried decoupage?