Before thinking too much about kids or no kids, it would be worth setting a budget and deciding what slice of the world you plan on visiting, as both of these will play big roles in what you can and can’t choose. Picking dates is also important, as generally, non-holiday periods and longer cruises have less kids.
The ships with most kids will include the likes of NCL, Carnival, RCCL, MSC, Costa and Disney. Disney has very good areas for avoiding the kids and is arguably more luxurious than the other more kid friendly lines, but it is also quite a bit more expensive.
Should it matter to you, Disney, RCCL and NCL are known for having some of the best evening shows in the industry.
On the next tier of less kids but still fairly mainstream and affordable, you could look at Celebrity, Princess and HAL. The clientele is generally older (especially in the case of HAL) and the entertainment more subdued.
I have a child, but I’m also a Celebrity fan as I like the styling of their newer ships and their food is pretty good (better I think than Disney), but on the flipside, their entertainment options could be improved.
Then, the next tier is the no-low kid options such as Oceania, Regent, Aramara, Crystal, Windstar etc, but be aware that these lines come at a cost. Some of them are quite inclusive with little need to pay any extras once onboard, but even then you need to crunch the numbers to check you’re getting what you pay for.
And lastly, to answer your question directly: Cruise Critic