Can you max both Paragon and Renegade points?

There are ways to max both paragon and renegade in ME1 and ME2 if you use the glitches described on the wiki page.

On Noveria. You are given a side mission leading you to speak to Lorik Qui'in, a turian, at the bar. A mission progression choice enables you to encourage him to testify in a court case. You can choose from either a Paragon or Renegade dialogue option if you have at least 5 points in charm and/or intimidate. Choosing either of these options will give you a reward of 24 Paragon or 25 Renegade points respectively. The conversation will end but you can talk to him again. Ask about a different topic (i.e. Matriarch Benezia), then choose "Another question". The option to convince him to testify will reappear. Repeat this for infinite Paragon and/or Renegade points. This bug appears to exist across all 3 platforms (Xbox360, PS3, PC). This bug still exists in Mass Effect Legendary Edition.

There are multiple ways to do so in both games. In ME1, you can also legitimately gain the paragon/renegade skill ranks as your skills carry over in a new game+ and there are points in the story where you automatically rank up in those skills.

Outside of exploits, its impossible to max both paragon and renegade in ME2 or 3, but you can max the skills in ME1 via new game +.

Currently, there are no known ways to max both in ME3, but it becomes less necessary as in ME3 your total rep can contribute to speech unlock checks rather than individual levels.