The best sports games like Skate 3 are Session: Skate Sim, Skater XL and Tony Hawk's Pro Skater 1 + 2. Below are 9, each with the reason it is here — and, at the end, what filtering to sports costs you.
Filtering to sports means you want the shape of a real game without necessarily wanting the rulebook. Most of the memorable ones throw the rules out entirely.
What you get: Something anybody can join. Arcade sports games are the easiest genre to hand to someone who does not play games.
What made Skate 3 worth playing in the first place is covered on the full list. This page is the sports part of that answer, and only the sports part.
The most committed successor — a stick per foot, and no score at all.
Flick-it taken further, with an enormous mod scene.
The other philosophy entirely: combos, timers and score.
Skating as a 2D precision platformer, and beautifully made.
Skating and shooting, with a stunning stylised look.
Downhill on a bike, procedural, and all about flow.
If the trick lines rather than the realism were the appeal.
Grinding a city with the style turned all the way up.
Where the whole grind-a-city genre starts.
Depth, in the arcade ones, and accessibility in the simulations. Very few sports games manage both.
The full list is on games like Skate 3 — 9 picks, no genre filter.
Session: Skate Sim. The most committed successor — a stick per foot, and no score at all.
No. Skate 3 released on the PlayStation 3, but a recommendation is only useful if you can play it, so the picks above span platforms and eras. What they share is the genre and the reason.
For the arcade picks, no — they do not use the real rules anyway. For the simulations, it helps a lot.
Usually not. The on-pitch changes between years are small and last year's version is a fraction of the price, unless you play the online team modes where the population moves across.
By hand. Each pick was written for the full Skate 3 list first, on what the game actually does, and this page is the part of that list that is sports — never a genre tag lookup, which is how "best racing games like Super Mario 64" used to be a page on this site.
Or read the sports guide for where to start in the genre generally.