I find that when I found my own religion, it doesn't seem worth the effort and time to convert my neighbors. It seems so much easier to just adopt someone else's religion. For instance, most of my games, the ai are all on just one or two religions, sometimes everyone on the continent is the same. If making friends is worth the trouble, it seems easier to let them convert you and everyone else, then to convert your whole island.

What are you thoughts?

You are forgetting the money that you get if you manage to spread your religion and build a shrine.

Yep, instead of missionares you can build units, and let someone else construct a shrine for you ;)

In some cases, with certain leaders, it may be worthwhile to get your own religion though - Saladin comes to mind - but I let others give examples on that regard, since I'm more of a warmongering player.

On a large continent a shrine of any religion isn't bad - just take one city in your empire later on and mass missionaries from it.

Early game, you found an early religion, or you don't worry about spreading it.

Many of my games emphasize an early great prophet to found christianity - depending on the AIs, where religion is founded, and trade networks, this often does not require much effort to spread to the AIs - which is unfortunate for me as I like to control the AP religion exclusively until I spread it strategically for the AP diplo win votes.

If you want to spread a religion and spread it to the AIs - found one early before the AIs have a religion, then create a trade network with ones without it - usually roads or coastal hookups with sailing. This gives a chance to get the religion to spread to them without missionaries, and they'll convert once it does. Usually a road to a river city with sailing or just a coastal city is good enough, if you get there first.

It gets harder on higher difficulties - I'll often not found one or found one and not use it except for a shrine later or to build the AP under.

What I usually do is found an early religion and build stonehenge. That gives me an early Great Priest that I use for a shrine. Then with trade networks and the shrine spreading my religion, I usually don't need a lot of missionaries.