In a nutshell
Falco is a very solid character with a lot of helpful tools. He has one of the best projectiles for keep-away, being able to gradually rack up damage while being difficult to approach. Falco is also dangerous up close. He has his hard to escape jab and of course his chaingrab, which will reliably tack on 35% on a grabbed opponent. Falco can also play well in the air. He has a reliable set of aerials that make engaging aerial combat with Falco quite difficult. If you want a character whose basic strategy is remarkably simple and effective, while being deadly when played at a high level, Falco may be the space pilot for you.
Falco currently clocks in at a very high 4th position out of 38 on the tier list, at the last position of the A Tier, and is now the highest-ranking veteran. He is top tier due to his great metagame, said follow-up ability, great projectile, long range in his reflector, and camping abilities. All this leads to very good matchups overall; while he has a few disadvantageous ones with the Ice Climbers and Pikachu, he is among only three characters to have an even matchup with Meta Knight. Similar to Marth, however, Falco still has problems from Melee; his recovery, while buffed, is still not particularly effective, and he can have difficulty landing his best finishing attacks.