I work in a Catholic church. Absolutely you can just turn up:
It's fine if you come once and don't come back.
It's fine if you come occasionally but never become regular (as long as you don't expect me to remember you and your life story, but that's just me, some people have better memories!)
It's fine to come to the services (Mass in our case) and not really join in, just sit and watch. Also fine to watch what everyone is doing and join in (although in a Catholic church you can't receive communion, you can do everything else). It's fine to ask for a book to follow along with the words (called a Missal) - your local church might not have any but it's fine to ask anyway.
It's fine to come in part way through and not stay for the whole thing - although use common courtesy by not sitting right at the front and making a big song and dance about leaving if you do! And obviously be a bit sensitive if the service you've walked in on is a funeral or wedding. It won't be a funeral on a Sunday and is very unlikely to be a wedding.
It's fine to introduce yourself and ask for help knowing what to do, or just say hello to the priest/minister for the sake of it. Also fine to skulk at the back and not talk to anyone. If there's coffee and biscuits afterwards it's fine to stay or not, whatever you want.
As a pp said, it's fine to come when there's no service on and just sit in the church or light a candle or whatever. But not all churches are open all day every day, so you might have to check before you travel (or just try the door if you're passing).
Basically, pretty much anything within the boundaries of general good manners is fine. You'd be very welcome. You might, unfortunately, happen to come across a tetchy busybody who doesn't make you feel welcome, but the vast majority of churchgoers would want to welcome you!