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I am curently doing about 30 repetitions for each excercise. When working my shoulders, bipeps or triceps I usually lift dumbbells of 6kg and am thinking of progressively raising it to 16kg.

Is this wrong? I feel the fatigue when getting around the 25th rep then I try to push it to 30.

Depends on your goals, but in most cases, it's way too high. It's definately endurance oriented. Look through this site in the Weight training section, and it will explain the differences in rep ranges. In a nutshell, most beginning trainees start out in the 8-15 rep range, being able to do 8 reps, but not more than 15, working progressively to 15, then adding weight and starting over again with 8 reps, and so on.
Tim

if you can do 30 reps you are going far too light
the optimal rep range depends on your goals
3-6...strength
8-12..muscle
12-15..weight loss

What about exercises which don't imply weights, for example push-ups, squats or abdominal exercises, is it safe to go beyond 15 reps ?

for muscle building i would try to find something for added resistance

we have 2 different types of muscle fibers-fast twitch and slow twitch...i cant remember which do what ,but the reason i mentioned it is because high reps are endurance training not srength....look at marathon runners they are very skinny and flat, now look at sprinters they are very lean
i know that resistance training and runner are two diiferenr things but that the correlation between the two in this case is pertinent.

like tim said check this whole site out
this whole web page is packed with an amazing wealth of information that i have found to be the only TRUE body building site on the web.....

You can accomplish alot simply by purchasing 1 weight plate, like say 25 lbs. Have someone put the plate on your back for your pushups, or you could do it yourself but its just a little more difficult...can be done with some manuervering though. For squats hold the plate overhead, if thats to easy do the squatting one leg at a time. You could also do wall squats with it, clutch it to your chest and sit against a wall like theres an imaginary chair there. Have your upper legs parrallel to the floor to start with, and hold that position for as long as you can. Trust me, it can be incredibly grueling towards the end! When you can do it for a minute, sit down to a lower position or do it with one leg at a time. Abdominals you do weighted crunches.

I find it a bit difficult to fully understand why somewhere around 30 reps would be a bit too much. I have searched through all the articles from this site and haven't found the exact answer for my question.

I perhaps should have mentioned before but I am not looking for high-performance body building but rather something like conditioning myself and keeping myself fit and healthy. I also want to put a lot of emphasis on flexibility.

I have practiced for a couple of months qwan-ki-do, a sort of martial art, for this goal I've just mentioned. I was very pleased with their fitness program, but I quit because I wasn't keen on wasting almost 1.5 hours (from the 3) with technical abilites, I just wanted the fitness part.

This being said, I remember doing for example around 100 pushups and also about 100 exercises in total for the abs, all in one set and with pretty good results to my physical condition (both muscle development, flexibility and the fact that I was feeling really fit). That's why I am a bit confused now that it is actually considered not the best thing to do over 15 reps.

Could you help, please.

The point of lifting weights is to inrease mass, increase strength, or increase coordination with weight.

Doing 30 reps means you are not using enough weight to do any of the above. You really can not build muscle doing that many reps.

All of the benefits of weightlifting are from the use of heavy weights that progressively overload muscles and cause growth.

For someone with your goals, I suggest doing 2-3 sets of 10-15 reps with a weight that is very challenging on the last couple reps.