What is out of date today is in tomorrow. I have many friends and relatives with wood trim and none plan a remodel or to change it out. While not like the wood of a decade ago, many new homes in my area have wood trim - it tends to be darker than in the past, but then it was dark in the 70's, lighter in the 90s - the trends go on and on, a merry go round of change. Design shows sometimes make people hate their homes - sometimes on purpose - marketing 101 - make people dislike their stuff so they will go out and buy new stuff.

Now, if you for your own sense of what you like, you want less wood, you could consider painting the trim only, leave doors and cabinets wood. This is a nice look. I have it in my own home and I like the brightness of the white combined with the warmth of the wood. Yes, I have to upkeep the trim - occasionally clean and give it some touch-ups. My trim was never pretty wood, so I did not have to make the hard decision to paint wood.

This is not my home - from This Old House and shows a nice combo of wood and white:

it won't chip if it's properly prepped and painted. If you want to paint it, clean it thoroughly to de-grease, lightly sand, wipe clean, and use an oil based primer. then use a quality trim paint for wood. Pro Classic and BM Advance are just two of the better ones. Farrow and Ball, Fine Paints of Europe, are some of the better ones.

as for whether or not to paint, it depends. is it the cheaper oak from the 70's and 80's or the fine quality quarter sawn oak from the early 1900's? Are you in a tract home or a craftsman? Big difference. If the former, paint it.