Although not new, a growing number of churches and people now do not claim any denominational affiliation, and call themselves simply "Christian" or "non-denominational". As they disclaim any label for their beliefs, it is impossible to say what they believe as a whole. However, there are some common beliefs that are often held by non-denominational churches. Most prominently, they cannot believe that their denomination is the whole church as Catholics and Eastern Orthodox believe, so they are going to be Protestant. Their disdain for inter-church leadership is also going to make them fairly congregational in their governance. Beyond that, it's hard to say for sure what any given non-denominational church believes. Most typically, the stereotype is that they are somewhere between Baptist and Pentecostal, but that is not always the case.
Typically the non-denominational label is claimed to avoid the negative connotations that certain people associate with certain denominations or to avoid the divisions that denominations cause. However, the effectiveness of this is questionable.
God doesn't like divisions, but a denomination is literally just a name. Simply calling yourself non-denominational doesn't remove the division; it just creates a new division with your new denomination of one. If your beliefs do align with those of a particular denomination, you're essentially just causing a division with that denomination by refusing to associate with them. If your beliefs don't align with any denomination, you still likely have other churches you are close to in beliefs.
It is also worth noting that you do not have to have common governance or be part of the same organization to be a denomination. A denomination is simply a group of churches that share common beliefs. Even if you don't associate with any other churches, if you have a set of common beliefs that you hold to, you are essentially the same denomination.
Unity in the church is a good and admirable goal, but it is not achieved by ignoring differences. Denominational labels have benefits, most prominently that they allow believers to find other believers who share their beliefs. By refusing to identify as a denomination, you are making it harder for other believers to find you and for you to find other believers. Instead of associating based on doctrinal beliefs, believers are forced to associate based on less important things like location, worship style, or how it feels to attend there. The Bible emphasizes the importance of unity, but it also emphasizes the importance of sound doctrine. We should not sacrifice one for the other.