Limits
The limit is dependent on both the server and the client used (and if applicable, also the proxy the server or the client is using).
On servers, the industry practice by most CDNs is to have the limit at 8192 bytes.
On browsers, it varies and we can see this be searching for max cookie size. But referencing http://browsercookielimits.squawky.net/ developers should not go beyond 4KB per domain and the safer number should be 2KB.
Cookies are also involved here as they are transmitted within request header.
The HTTP 1.1 specs section 3.2.1 provide warning on this topic,
Note: Servers ought to be cautious about depending on URI lengths
above 255 bytes, because some older client or proxy
implementations might not properly support these lengths.
Errors
If the limit is exceeded the following can occur,
Server tuncates or responds with an HTTP 414 error.
Server truncates or responds with an HTTP 413 error.
...
References
Good response on maximum http request - https://stackoverflow.com/questions/2659952/maximum-length-of-http-get-request