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The Golf Club has just hit Early Access on Steam, and it looks to be pretty sweet.

Golf Club. I really think it is fun.

There was a game on the original XBOX that was fantastic. One sec... Links 2004. Showed a lot of promise but never caught on. Also, SimGolf if it ever gets released again was amazing.

If you aren't too picky about the content, maybe Pangya? I've played on PSP and Wii, and enjoyed it there. The PC version looks to be a free to play title, with the kind of real cash unlocks that would result in.

Scores on GameFAQs look good.

wii sports resort

I recommend pangya But unfortunately, it is ridden with cheaters.

I'll be trying golf club in steam's early access soon. Might want to try it out also

Worms Crazy Golf

Look in Nintendo games.

i actually had a lot of fun with the tiger woods ones in my wii, it got better when the new controller arrived with better sensors, i remember that the last one i played even had a crazy mode that you played golf with a frisbee xD it was fun i think it was tiger woods 2012 or something like that in wii... in computer i dont have idea... just played worms crazy golf and its hilarious XD

my favourite one is Tiger Woods PGA Tour 08. Overall all of these tour games are pretty the same, all are good, at least for me. Nothing is better than the real thing, but for gaming I like these ones.
There's a game called Perfect Golf on greenlight. Looks awesome, can't wait till it comes out

Mario Golf for Nintendo 64. Play on PC with Project64, Nintendo 64 emulator for Windows.

I can't recommend a good one, but stay far away from "Swing Away Golf" for Playstation 2. Unless you want caddie advice such as "You hit too hard".

Shot Online might not quite count as modern (especially in terms of graphics) but it's my personal favourite and definitely fits the pick-up-and-play style you want.