Is free the only requirement? What kind of games do you like, what consoles do you have, how long should the speedrun be, do you like glitches, do you like popular or quiet games? There needs to be more info, otherwise nobody will be able to give you a good recommendation.
If you play on PC, you can try any of the web games on the site, they are all free: https://www.speedrun.com/games#platform=Web&orderby=mostactive&unofficial=on
Other than that, you will have to be much more specific.
Web Games Are Where Its At I Suggest Black Box Jumper its A Simple Platforming Game WIth A Small Community Try It Out!
OP hasn't responded, so I'll just list some good webgames:
Red Ball: The red ball series has a lot of comprehensive guides and a very active community, as well as category extensions and ILs, so there is a lot of variety https://www.speedrun.com/redball#platform=&orderby=oldest&unofficial=on
Eddynardo: The eddynardo games are short platforming games that have a simple mechanic that creates very unique challenge. For casual players, the mixture of puzzles and difficult gameplay makes it very fun, and the movement makes it very popular for speedrunning. https://www.speedrun.com/eddynardo (Dozenbear, another eddynardo game, isn't included on the series page. Here is the link: https://www.speedrun.com/dozenbear )
Grey-Box Testing: I might be a bit biased, but this game, despite being simple, is very easy to pick up and get a top time within a few days. There is also a category extensions leaderboard if you want more variety. The community has also created several mods for the game, including an autosplitter, a portal gun, and a mod menu, which are fun to mess around with. If you like glitchy games, this is for you. https://www.speedrun.com/gbt https://www.speedrun.com/gbtce
Celeste Classic 2: The sequel to celeste classic, this game is very technical and requires a lot of mastery over the game to go fast. It's incredibly satisfying and fun to mess around with momentum, so if you like very technical or focus-intensive games, try this one out. https://www.speedrun.com/celeste_classic_2
60 Second Burger Run: Short flash game that takes less than 60 seconds to complete. Pretty simple game, nothing really that special about it. https://www.speedrun.com/60sbr
Since OP deleted his post, I think we can assume that he’s no longer looking for game recommendations.