Can I visit other countries if I get deported from the US? [duplicate]

So, let's say I get deported from the US for doing something illegal (could be a crime, could be anything) and the deportation document says I cannot enter for the next 10 years. Now, in these 10 years, can I visit other countries? Of course the logical answer is, "Yes, if the country you want to go to will admit you".

But, here's the tricky part, how hard does it become to get visas to other countries when you've been deported from the US? Will other countries' visa application ask me about my deportation or travel history (A question like "Have you ever been deported from any country, if yes, please list them" is highly probable")

Also, how will it impact my travel to the UK, Canada, Australia and New Zealand? I ask because US along with these countries is collectively called the "Five Eyes", a term that US Govt uses to list major English speaking nations of the world., not to forget they have strong ties and diplomatic relations with each other.